Geometry Of Submanifolds And Homogeneous Spaces
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Geometry Of Submanifolds And Homogeneous Spaces
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Author : Andreas Arvanitoyeorgos
language : en
Publisher: MDPI
Release Date : 2020-01-03
Geometry Of Submanifolds And Homogeneous Spaces written by Andreas Arvanitoyeorgos and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.
The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.
Geometry Of Submanifolds And Homogeneous Spaces
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Author : Andreas Arvanitogeōrgos
language : en
Publisher:
Release Date : 2019
Geometry Of Submanifolds And Homogeneous Spaces written by Andreas Arvanitogeōrgos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Submanifolds And Holonomy
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Author : Jurgen Berndt
language : en
Publisher: CRC Press
Release Date : 2016-02-22
Submanifolds And Holonomy written by Jurgen Berndt and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-22 with Mathematics categories.
Submanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor.New to the Second EditionNew chapter on normal holonom
Geometry Of Homogeneous Spaces And Submanifolds
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Author : Hiroyuki Tasaki
language : en
Publisher:
Release Date : 1998
Geometry Of Homogeneous Spaces And Submanifolds written by Hiroyuki Tasaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Surfaces In Classical Geometries
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Author : Gary R. Jensen
language : en
Publisher: Springer
Release Date : 2016-04-20
Surfaces In Classical Geometries written by Gary R. Jensen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-20 with Mathematics categories.
Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed. Its application in many areas helps to connect the various geometries and to uncover many deep relationships, such as the Lawson correspondence. The nearly 300 problems and exercises range from simple applications to open problems. Exercises are embedded in the text as essential parts of the exposition. Problems are collected at the end of each chapter; solutions to select problems are given at the end of the book. Mathematica®, MatlabTM, and Xfig are used to illustrate selected concepts and results. The careful selection of results serves to show the reader how to prove the most important theorems in the subject, which may become the foundation of future progress. The book pursues significant results beyond the standard topics of an introductory differential geometry course. A sample of these results includes the Willmore functional, the classification of cyclides of Dupin, the Bonnet problem, constant mean curvature immersions, isothermic immersions, and the duality between minimal surfaces in Euclidean space and constant mean curvature surfaces in hyperbolic space. The book concludes with Lie sphere geometry and its spectacular result that all cyclides of Dupin are Lie sphere equivalent. The exposition is restricted to curves and surfaces in order to emphasize the geometric interpretation of invariants and other constructions. Working in low dimensions helps students develop a strong geometric intuition. Aspiring geometers will acquire a working knowledge of curves and surfaces in classical geometries. Students will learn the invariants of conformal geometry and how these relate to the invariants of Euclidean, spherical, and hyperbolic geometry. They will learn the fundamentals of Lie sphere geometry, which require the notion of Legendre immersions of a contact structure. Prerequisites include a completed one semester standard course on manifold theory.
From Frenet To Cartan The Method Of Moving Frames
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Author : Jeanne N. Clelland
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-03-29
From Frenet To Cartan The Method Of Moving Frames written by Jeanne N. Clelland and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-29 with Mathematics categories.
The method of moving frames originated in the early nineteenth century with the notion of the Frenet frame along a curve in Euclidean space. Later, Darboux expanded this idea to the study of surfaces. The method was brought to its full power in the early twentieth century by Elie Cartan, and its development continues today with the work of Fels, Olver, and others. This book is an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces, including Euclidean, Minkowski, equi-affine, and projective spaces. Later chapters include applications to several classical problems in differential geometry, as well as an introduction to the nonhomogeneous case via moving frames on Riemannian manifolds. The book is written in a reader-friendly style, building on already familiar concepts from curves and surfaces in Euclidean space. A special feature of this book is the inclusion of detailed guidance regarding the use of the computer algebra system Maple™ to perform many of the computations involved in the exercises.
Lie Groups And Geometric Aspects Of Isometric Actions
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Author : Marcos M. Alexandrino
language : en
Publisher: Springer
Release Date : 2015-05-22
Lie Groups And Geometric Aspects Of Isometric Actions written by Marcos M. Alexandrino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-22 with Mathematics categories.
This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.
Symmetries And Overdetermined Systems Of Partial Differential Equations
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Author : Michael Eastwood
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-23
Symmetries And Overdetermined Systems Of Partial Differential Equations written by Michael Eastwood and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-23 with Mathematics categories.
This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
The Mathematical Heritage Of C F Gauss
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Author : George M Rassias
language : en
Publisher: World Scientific
Release Date : 1991-09-30
The Mathematical Heritage Of C F Gauss written by George M Rassias and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-30 with categories.
This volume is a collection of original and expository papers in the fields of Mathematics in which Gauss had made many fundamental discoveries. The contributors are all outstanding in their fields and the volume will be of great interest to all research mathematicians, research workers in the history of science, and graduate students in Mathematics and Mathematical Physics.
Geometric Continuum Mechanics
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Author : Reuven Segev
language : en
Publisher: Springer Nature
Release Date : 2020-05-13
Geometric Continuum Mechanics written by Reuven Segev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Mathematics categories.
This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.