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Differential Geometry Of Submanifolds
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Book Synopsis Geometry of Submanifolds by : Bang-Yen Chen
Download or read book Geometry of Submanifolds written by Bang-Yen Chen and published by Courier Dover Publications. This book was released on 2019-06-12 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and their applications, and total mean curvature of a submanifold. Suitable for graduate students and mathematicians in the area of classical and modern differential geometries, the treatment is largely self-contained. Problems sets conclude each chapter, and an extensive bibliography provides background for students wishing to conduct further research in this area. This new edition includes the author's corrections.
Book Synopsis Projective Differential Geometry of Submanifolds by : M.A. Akivis
Download or read book Projective Differential Geometry of Submanifolds written by M.A. Akivis and published by Elsevier. This book was released on 1993-06-30 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations. Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.
Book Synopsis Differential Geometry Of Warped Product Manifolds And Submanifolds by : Chen Bang-yen
Download or read book Differential Geometry Of Warped Product Manifolds And Submanifolds written by Chen Bang-yen and published by World Scientific. This book was released on 2017-05-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson–Walker models, are warped product manifolds. The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson–Walker's and Schwarzschild's. The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Book Synopsis Differential Geometry of Lightlike Submanifolds by : Krishan L. Duggal
Download or read book Differential Geometry of Lightlike Submanifolds written by Krishan L. Duggal and published by Springer Science & Business Media. This book was released on 2011-02-02 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.
Book Synopsis New Ideas in Differential Geometry of Submanifolds by : IUrii Akhmetovich Aminov
Download or read book New Ideas in Differential Geometry of Submanifolds written by IUrii Akhmetovich Aminov and published by . This book was released on 2000 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry of Submanifolds by : K. Kenmotsu
Download or read book Differential Geometry of Submanifolds written by K. Kenmotsu and published by Springer. This book was released on 2007-01-05 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symposium on the Differential Geometry of Submanifolds by : Luc Vrancken
Download or read book Symposium on the Differential Geometry of Submanifolds written by Luc Vrancken and published by Lulu.com. This book was released on 2008-06-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).
Book Synopsis Differential Geometry of Submanifolds by : K. Kenmotsu
Download or read book Differential Geometry of Submanifolds written by K. Kenmotsu and published by . This book was released on 2014-09-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry and Topology of Submanifolds, X by : Weihuan Chen
Download or read book Geometry and Topology of Submanifolds, X written by Weihuan Chen and published by World Scientific. This book was released on 2000 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: http://www.worldscientific.com/worldscibooks/10.1142/4569
Book Synopsis Geometry And Topology Of Submanifolds Viii by : Ignace Van De Woestyne
Download or read book Geometry And Topology Of Submanifolds Viii written by Ignace Van De Woestyne and published by World Scientific. This book was released on 1996-10-25 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings consists of papers presented at the international meeting of Differential Geometry and Computer Vision held in Norway and of international meetings on Pure and Applied Differential Geometry held in Belgium. This volume is dedicated to Prof Dr Tom Willmore for his contribution to the development of the domain of differential geometry. Furthermore, it contains a survey on recent developments on affine differential geometry, including a list of publications and a problem list.
Book Synopsis Differential Geometry of Varieties with Degenerate Gauss Maps by : Maks A. Akivis
Download or read book Differential Geometry of Varieties with Degenerate Gauss Maps written by Maks A. Akivis and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.
Book Synopsis Some Contributions to the Differential Geometry of Submanifolds by : Barbara Opozda
Download or read book Some Contributions to the Differential Geometry of Submanifolds written by Barbara Opozda and published by . This book was released on 1992 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry of Submanifolds and its Related Topics by : Sadahiro Maeda
Download or read book Differential Geometry of Submanifolds and its Related Topics written by Sadahiro Maeda and published by World Scientific. This book was released on 2013-10-23 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form. Contents:Homogeneous Submanifolds and Homogeneous Curves in Space Forms (S Maeda)Injectivity Property of Regular Curves and a Sphere Theorem (O Kobayashi)A Family of Complete Minimal Surfaces of Finite Total Curvature with Two Ends (S Fujimori and T Shoda)Minimal Surfaces in the Anti-De Sitter Spacetime (T Ichiyama and S Udagawa)Extrinsic Circular Trajectories on Geodesic Spheres in a Complex Projective Space (T Adachi)Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces (Y Ohnita)Some Real Hypersurfaces of Complex Projective Space (T Hamada)Contact Metric Hypersurfaces in Complex Space Forms (J T Cho and J Inoguchi)Non-Homogeneous η-Einstein Real Hypersurfaces in a 2-Dimensional Nonflat Complex Space Form (K Okumura)Sectional Curvatures of Ruled Real Hypersurfaces in a Nonflat Complex Space Form (H Tanabe and S Maeda)Totally Geodesic Köhler Immersions into a Complex Space Form, and a Non-Existence Theorem for Hessian Metrics of Positive Constant Hessian Sectional Curvature (T Noda and N Boumuki)Archimedean Theorems and W-Curves (D-S Kim and Y H Kim)On the Construction of Cohomogeneity One Special Lagrangian Submanifolds in the Cotangent Bundle of the Sphere (K Hashimoto)Self-Shrinkers of the Mean Curvature Flow (Q-M Cheng and Y Peng)Spectrum of Poly-Laplacian and Fractional Laplacian (L Zeng)Flat Centroaffine Surfaces with Non-Semisimple Tchebychev Operator (A Fujioka)The Total Absolute Curvature of Open Curves in EN (K Enomoto and J Itoh)Antipodal Sets of Compact Symmetric Spaces and the Intersection of Totally Geodesic Submanifolds (M S Tanaka)A Note on Symmetric Triad and Hermann Action (O Ikawa)Some Topics of Homogeneous Submanifolds in Complex Hyperbolic Spaces (T Hashinaga, A Kubo and H Tamaru)Austere Hypersurfaces in 5-Sphere and Real Hypersurfaces in Complex Projective Plane (J T Cho and M Kimura)On the Minimality of Normal Bundles in the Tangent Bundles Over the Complex Space Forms (T Kajigaya)Over-Determined Systems on Surfaces (N Ando) Readership: Researchers in differential geometry. Keywords:Minimal Surfaces;Morse Index;Real Hypersurfaces;Non-flat Complex Space Forms;Hopf Hypersurfaces;Symmetric Spaces;Homogeneous CurvesKey Features:Interesting papers on the theory of real hypersurfaces and the theory of minimal surfacesFeatures prominent contributors such as Y Ohnita, Q-M Cheng and O Kobayashi
Book Synopsis Geometry and Topology of Submanifolds X by : W H Chen
Download or read book Geometry and Topology of Submanifolds X written by W H Chen and published by World Scientific. This book was released on 2000-11-07 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Progress in Affine Differential Geometry — Problem List and Continued Bibliography (T Binder & U Simon)On the Classification of Timelike Bonnet Surfaces (W H Chen & H Z Li)Affine Hyperspheres with Constant Affine Sectional Curvature (F Dillen et al.)Geometric Properties of the Curvature Operator (P Gilkey)On a Question of S S Chern Concerning Minimal Hypersurfaces of Spheres (I Hiric( & L Verstraelen)Parallel Pure Spinors on Pseudo-Riemannian Manifolds (I Kath)Twistorial Construction of Spacelike Surfaces in Lorentzian 4-Manifolds (F Leitner)Nirenberg's Problem in 90's (L Ma)A New Proof of the Homogeneity of Isoparametric Hypersurfaces with (g,m) = (6, 1) (R Miyaoka)Harmonic Maps and Negatively Curved Homogeneous Spaces (S Nishikawa)Biharmonic Morphisms Between Riemannian Manifolds (Y L Ou)Intrinsic Properties of Real Hypersurfaces in Complex Space Forms (P J Ryan)On the Nonexistence of Stable Minimal Submanifolds in Positively Pinched Riemannian Manifolds (Y B Shen & H Q Xu)Geodesic Mappings of the Ellipsoid (K Voss)η-Invariants and the Poincaré-Hopf Index Formula (W Zhang)and other papers Readership: Researchers in differential geometry and topology. Keywords:Conference;Proceedings;Berlin (Germany);Beijing (China);Geometry;Topology;Submanifolds X;Differential Geometry;Dedication
Book Synopsis New Ideas in Differential Geometry of Submanifolds by : I︠U︡riĭ Akhmetovich Aminov
Download or read book New Ideas in Differential Geometry of Submanifolds written by I︠U︡riĭ Akhmetovich Aminov and published by . This book was released on 2000 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry and Topology of Submanifolds IX by : F. Defever
Download or read book Geometry and Topology of Submanifolds IX written by F. Defever and published by World Scientific. This book was released on 1999 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: http://www.worldscientific.com/worldscibooks/10.1142/4122
Book Synopsis Geometry of CR-Submanifolds by : Aurel Bejancu
Download or read book Geometry of CR-Submanifolds written by Aurel Bejancu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can us;; Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
