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On Parametric Surfaces With Constant Mean Curvature Along Given Smarandache Curves In Lie Group
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Book Synopsis On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group by : Zuhal Kucukarslan Yuzbasi
Download or read book On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group written by Zuhal Kucukarslan Yuzbasi and published by Infinite Study. This book was released on 2022-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the ๐๐, ๐๐ต, and ๐๐ต Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given ๐๐, ๐๐ต, and ๐๐ต Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curvatures of the resulting surfaces at a constant value. Finally, some examples are provided.
Book Synopsis Surfaces with Constant Mean Curvature by : Katsuei Kenmotsu
Download or read book Surfaces with Constant Mean Curvature written by Katsuei Kenmotsu and published by American Mathematical Soc.. This book was released on 2003 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.
Book Synopsis Special Smarandache Ruled Surfaces According to Flc Frame by : Suleyman Senyurt
Download or read book Special Smarandache Ruled Surfaces According to Flc Frame written by Suleyman Senyurt and published by Infinite Study. This book was released on 2023-01-01 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, we introduce some special ruled surfaces according to the Flc frame of a given polynomial curve. We name these ruled surfaces as Smarandache ruled surfaces and provide their characteristics such as Gauss and mean curvatures in order to specify their developability and minimality conditions. Moreover, we examine the conditions if the parametric curves of the surfaces are asymptotic, geodesic or curvature line. Such conditions are also argued in terms of the developability and minimality conditions. Finally, we give an example and picture the corresponding graphs of ruled surfaces by using Maple17.
Book Synopsis Investigation of Special Type-ฮ Smarandache Ruled Surfaces Due to Rotation Minimizing Darboux Frame by : Emad Solouma
Download or read book Investigation of Special Type-ฮ Smarandache Ruled Surfaces Due to Rotation Minimizing Darboux Frame written by Emad Solouma and published by Infinite Study. This book was released on 2024-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study begins with the construction of type-ฮ Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced.
Book Synopsis Space-like Surfaces of Constant Mean Curvature in de Sitter 3-space S31 by : Sungwook Lee
Download or read book Space-like Surfaces of Constant Mean Curvature in de Sitter 3-space S31 written by Sungwook Lee and published by . This book was released on 2002 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Surfaces of Constant Mean Curvature in Constant Curvature Manifolds by : D. Hoffmann
Download or read book Surfaces of Constant Mean Curvature in Constant Curvature Manifolds written by D. Hoffmann and published by . This book was released on 1971 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES) by : Linfan MAO
Download or read book MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES) written by Linfan MAO and published by Infinite Study. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
Book Synopsis A First Course in Differential Geometry by : Vaisman
Download or read book A First Course in Differential Geometry written by Vaisman and published by CRC Press. This book was released on 1983-12-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.
Book Synopsis Noether's Theorems by : Gennadi Sardanashvily
Download or read book Noether's Theorems written by Gennadi Sardanashvily and published by Springer. This book was released on 2016-03-18 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
Book Synopsis Differential Geometry by : Wolfgang Kรผhnel
Download or read book Differential Geometry written by Wolfgang Kรผhnel and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.
Book Synopsis Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics by : Linfan Mao
Download or read book Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics written by Linfan Mao and published by Infinite Study. This book was released on 2011 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tensors and Their Applications by : Nazrul Islam
Download or read book Tensors and Their Applications written by Nazrul Islam and published by New Age International. This book was released on 2006-12 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Book Is Written Is In Easy-To-Read Style With Corresponding Examples. The Main Aim Of This Book Is To Precisely Explain The Fundamentals Of Tensors And Their Applications To Mechanics, Elasticity, Theory Of Relativity, Electromagnetic, Riemannian Geometry And Many Other Disciplines Of Science And Engineering, In A Lucid Manner. The Text Has Been Explained Section Wise, Every Concept Has Been Narrated In The Form Of Definition, Examples And Questions Related To The Concept Taught. The Overall Package Of The Book Is Highly Useful And Interesting For The People Associated With The Field.
Book Synopsis Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science by : Florentin Smarandache
Download or read book Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science written by Florentin Smarandache and published by Infinite Study. This book was released on 2006-01-01 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!
Book Synopsis Combinatorial Geometry with Applications to Field Theory by : Linfan Mao
Download or read book Combinatorial Geometry with Applications to Field Theory written by Linfan Mao and published by Infinite Study. This book was released on 2009 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is motivated with surveying mathematics and physics by CC conjecture, i.e., a mathematical science can be reconstructed from or made by combinatorialization. Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields with their combinatorial generalization, also with discussions on fundamental questions in epistemology. All of these are valuable for researchers in combinatorics, topology, differential geometry, gravitational or quantum fields.
Book Synopsis The Oxford Solid State Basics by : Steven H. Simon
Download or read book The Oxford Solid State Basics written by Steven H. Simon and published by Oxford University Press. This book was released on 2013-06-20 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a first undergraduate textbook in Solid State Physics or Condensed Matter Physics. While most textbooks on the subject are extremely dry, this book is written to be much more exciting, inspiring, and entertaining.
Download or read book Prime Numbers written by Richard Crandall and published by Springer Science & Business Media. This book was released on 2006-04-07 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field
Book Synopsis Quantization in Astrophysics, Brownian Motion, and Supersymmetry by : Florentin Smarandache
Download or read book Quantization in Astrophysics, Brownian Motion, and Supersymmetry written by Florentin Smarandache and published by Infinite Study. This book was released on 2007 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
