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 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 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 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 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.
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.
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.
Download or read book Investigation of Special Type 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-Π 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.
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:
Download or read book Surfaces of Constant Mean Curvature in Space Forms written by Bennett Palmer and published by . This book was released on 1986 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book On Nonparametric Surfaces of Constant Mean Curvature written by Fei-tsen Liang and published by . This book was released on 1986 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Contributions to the Theory of Surfaces of Constant Mean Curvature written by Eamon Barrett and published by . This book was released on 1966 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Surfaces of Constant Mean Curvature written by Joseph Albert Wolf and published by . This book was released on 196? with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Surfaces with Constant Mean Curvature written by Lawrence E. Schmidt and published by . This book was released on 19?? with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Loop Group Methods for Constant Mean Curvature Surfaces written by 祥一·藤森 and published by . This book was released on 2005 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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:
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.
Download or read book Differential Geometry written by Wolfgang Kühnel 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.
