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Author : Maurice Leslie Hartung
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.:/5 (89 download)
Download or read book Geodesics on Surfaces of Constant Curvature written by Maurice Leslie Hartung and published by . This book was released on 1926 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Veasna Chiek
Publisher :
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4.:/5 (123 download)
Download or read book Geodesic on Surfaces of Constant Gaussian Curvature written by Veasna Chiek and published by . This book was released on 2006 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best paths.
Author : Harry Ernest Rauch
Publisher :
ISBN 13 :
Total Pages : 76 pages
Book Rating : 4.X/5 (1 download)
Download or read book Geodesics and Curvature in Differential Geometry in the Large written by Harry Ernest Rauch and published by . This book was released on 1959 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Merrick Leigh Sterling
Publisher :
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.:/5 (646 download)
Download or read book Geometric Coding of Geodesics on Surfaces of Constant Negative Curvature written by Merrick Leigh Sterling and published by . This book was released on 2005 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W Klingenberg
Publisher :
ISBN 13 : 9783642618826
Total Pages : 248 pages
Book Rating : 4.6/5 (188 download)
Download or read book Lectures on Closed Geodesics written by W Klingenberg and published by . This book was released on 1978-01-01 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. L. Besse
Publisher : Springer Science & Business Media
ISBN 13 : 3642618766
Total Pages : 271 pages
Book Rating : 4.6/5 (426 download)
Download or read book Manifolds all of whose Geodesics are Closed written by A. L. Besse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: X 1 O S R Cher lecteur, J'entre bien tard dans la sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un general epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie. Je suis entiche de geometrie et c'est d'elle dontje voudrais vous parler, oh! certes pas de toute la geometrie, mais de celle que fait l'artisan qui taille, burine, amene, gauchit, peaufine les formes. Mon interet pour le probleme dont je veux vous entretenir ici, je le dois a un ami ebeniste. En effet comme je rendais un jour visite il cet ami, je le trouvai dans son atelier affaire a un tour. Il se retourna bientot, puis, rayonnant, me tendit une sorte de toupie et me dit: {laquo}Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: {laquo}Regardez! Si vous prenez ce collier de laine et si vous le maintenez fermement avec un doigt place n'importe ou sur la toupie, eh bien! la toupie passera toujours juste en son interieur, sans laisser le moindre espace.)) Je rentrai chez moi, fort etonne, car sa toupie etait loin d'etre une boule. Je me mis alors au travail ...
Author : Elsa Abbena
Publisher : CRC Press
ISBN 13 : 1351992201
Total Pages : 1024 pages
Book Rating : 4.3/5 (519 download)
Download or read book Modern Differential Geometry of Curves and Surfaces with Mathematica written by Elsa Abbena and published by CRC Press. This book was released on 2017-09-06 with total page 1024 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.
Author : M. Abate
Publisher : Springer Science & Business Media
ISBN 13 : 8847019419
Total Pages : 407 pages
Book Rating : 4.8/5 (47 download)
Download or read book Curves and Surfaces written by M. Abate and published by Springer Science & Business Media. This book was released on 2012-06-11 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincaré-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3.
Author : Katsuhiro Shiohama
Publisher : Elsevier Science & Technology
ISBN 13 :
Total Pages : 506 pages
Book Rating : 4.:/5 (42 download)
Download or read book Geometry of Geodesics and Related Topics written by Katsuhiro Shiohama and published by Elsevier Science & Technology. This book was released on 1984 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume in the Japanese symposia series surveys recent advances in five areas of Geometry, namely Closed geodesics, Geodesic flows, Finiteness and uniqueness theorems for compact Riemannian manifolds, Hadamard manifolds, and Topology of complete noncompact manifolds.
Author : Dorairaj Somasundaram
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9781842651827
Total Pages : 472 pages
Book Rating : 4.6/5 (518 download)
Download or read book Differential Geometry written by Dorairaj Somasundaram and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry: A First Course is an introduction to the classical theory of space curves and surfaces offered in graduate and postgraduate courses in mathematics. Based on Serret-Frenet formulae, the theory of space curves is developed and concluded with a detailed discussion on fundamental existence theorem. The theory of surfaces includes the first fundamental form with local intrinsic properties, geodesics on surfaces, the second fundamental form with local non-intrinsic properties and the fundamental equations of the surface theory with several applications.
Author : Luther Pfahler Eisenhart
Publisher :
ISBN 13 :
Total Pages : 524 pages
Book Rating : 4.:/5 (4 download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1909 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart, first published in 1909, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Author : Luther Pfahler Eisenhart
Publisher :
ISBN 13 :
Total Pages : 500 pages
Book Rating : 4.A/5 ( download)
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1909 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart, first published in 1909, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Author : Peter Buser
Publisher : Springer Science & Business Media
ISBN 13 : 0817649921
Total Pages : 473 pages
Book Rating : 4.8/5 (176 download)
Download or read book Geometry and Spectra of Compact Riemann Surfaces written by Peter Buser and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.
Author :
Publisher : CUP Archive
ISBN 13 :
Total Pages : 566 pages
Book Rating : 4./5 ( download)
Download or read book Lectures on the Differential Geometry of Curves Ans Surfaces written by and published by CUP Archive. This book was released on with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.N. Pressley
Publisher : Springer Science & Business Media
ISBN 13 : 1447136969
Total Pages : 336 pages
Book Rating : 4.4/5 (471 download)
Download or read book Elementary Differential Geometry written by A.N. Pressley and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.
Author : Bernard H. Lavenda
Publisher : World Scientific
ISBN 13 : 9814340480
Total Pages : 695 pages
Book Rating : 4.8/5 (143 download)
Download or read book A New Perspective on Relativity written by Bernard H. Lavenda and published by World Scientific. This book was released on 2012 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting off from noneuclidean geometries, apart from the method of Einstein's equations, this book derives and describes the phenomena of gravitation and diffraction. A historical account is presented, exposing the missing link in Einstein's construction of the theory of general relativity: the uniformly rotating disc, together with his failure to realize, that the Beltrami metric of hyperbolic geometry with constant curvature describes exactly the uniform acceleration observed. This book also explores these questions: * How does time bend? * Why should gravity propagate at the speed of light? * How does the expansion function of the universe relate to the absolute constant of the noneuclidean geometries? * Why was the Sagnac effect ignored? * Can Maxwell's equations accommodate mass? * Is there an inertia due solely to polarization? * Can objects expand in elliptic geometry like they contract in hyperbolic geometry?
Author : Yanwen Luo
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.6/5 (647 download)
Download or read book The Spaces of Shapes and Geodesic Triangulations on Surfaces written by Yanwen Luo and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the geometry and topology of surfaces has been well-established during the last century from various perspectives. In recent developments of discrete differential geometry, mathematicians started to think rigorously about the discrete counterparts of concepts in the smooth setting, including triangulations, metrics, curvatures. We study the geometry of discrete surfaces via discrete metrics, discrete curvatures, and discrete conformal maps, not only as approximations to the smooth counterparts, but as geometric objects in their own right. They provide fast algorithms in computer graphics, and also a parallel theory, such as discrete uniformization theorems.This thesis is concerned with these types of problems. We study the geometry and topology of "shape" spaces of different geometric objects, including high genus surfaces in R3 and geodesic triangulations on surfaces with constant curvature. In Chapter 2, we study the global comparison problem for two surfaces with the same high genus, constructing a metric on the shape space and producing a correspondence between two given shapes. This leads to an algorithm to compute the distance between a pair of shapes via energy minimization. In Chapter 3, we consider the topology of the space of geodesic triangulations on a surface with a fixed combinatorial type in a fixed isotopy class, which can be regarded as a discrete version of the group of surface diffeomorphisms. We show that these spaces, after appropriate normalization, are contractible when the surface is a convex polygon. Furthermore, we provide an algorithm to generate geodesic triangulations when the surface is a star-shaped polygon.
