Differential Geometry From A Singularity Theory Viewpoint
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Differential Geometry From A Singularity Theory Viewpoint
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Author : Shyuichi Izumiya
language : en
Publisher: World Scientific
Release Date : 2015-10-29
Differential Geometry From A Singularity Theory Viewpoint written by Shyuichi Izumiya and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-29 with Mathematics categories.
Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.
Differential Geometry Of Curves And Surfaces With Singularities
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Author : Masaaki Umehara
language : en
Publisher:
Release Date : 2021
Differential Geometry Of Curves And Surfaces With Singularities written by Masaaki Umehara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Curves on surfaces categories.
"This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields - singularity theory and differential geometry. The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space. In particular, by presenting the singular curvature, which originated through research by the authors, the Gauss-Bonnet theorem for surfaces is generalized to those with singularities. The Gauss-Bonnet theorem is intrinsic in nature, that is, it is a theorem not only for surfaces but also for 2-dimensional Riemannian manifolds. The book also elucidates the notion of Riemannian manifolds with singularities. These topics, as well as elementary descriptions of proofs of the recognition theorems, cannot be found in other books. Explicit examples and models are provided in abundance, along with insightful explanations of the underlying theory as well. Numerous figures and exercise problems are given, becoming strong aids in developing an understanding of the material. Readers will gain from this text a unique introduction to the singularities of curves and surfaces from the viewpoint of differential geometry, and it will be a useful guide for students and researchers interested in this subject"--
Differential Geometry From The Viewpoint Of Lagrangian Or Legendrian Singularity Theory
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Author : Shyuichi Izumiya
language : en
Publisher:
Release Date : 2005
Differential Geometry From The Viewpoint Of Lagrangian Or Legendrian Singularity Theory written by Shyuichi Izumiya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Differential Geometry From The Viewpoint Of Lagrangian Or Legendrian Singularity Theory
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Author :
language : en
Publisher:
Release Date : 2005
Differential Geometry From The Viewpoint Of Lagrangian Or Legendrian Singularity Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Curves And Singularities
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Author : J. W. Bruce
language : en
Publisher: Cambridge University Press
Release Date : 1992-11-26
Curves And Singularities written by J. W. Bruce and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-26 with Mathematics categories.
The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors take a novel approach by casting the theory into a new light, that of singularity theory. The second edition of this successful textbook has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added that covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to the modern theories of catastrophes and singularities.
Applications Of Singularity Theory Of Differential Equations And Differential Geometry
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Author : Masatomo Takahashi
language : en
Publisher:
Release Date : 2009
Applications Of Singularity Theory Of Differential Equations And Differential Geometry written by Masatomo Takahashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Differential Geometry And Lie Groups
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Author : Jean Gallier
language : en
Publisher: Springer
Release Date : 2021-08-16
Differential Geometry And Lie Groups written by Jean Gallier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-16 with Mathematics categories.
This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.
Geometric Theory Of Singular Phenomena In Partial Differential Equations
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Author : Jean Pierre Bourguignon
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-28
Geometric Theory Of Singular Phenomena In Partial Differential Equations written by Jean Pierre Bourguignon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-28 with Mathematics categories.
This book gathers together papers from a workshop held in Cortona, Italy. The contributions come from a group of outstanding mathematicians and together they cover the most recent advances in the geometric theory of singular phenomena of partial differential equations occurring in real and complex differential geometry. This volume will be of great interest to all those whose research interests lie in real and complex differential geometry, partial differential equations, and gauge theory.
The Theory Of Singularities And Its Applications
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher: Cambridge University Press
Release Date : 1991-05-31
The Theory Of Singularities And Its Applications written by Vladimir Igorevich Arnolʹd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-05-31 with Mathematics categories.
In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.
Theory Of Singularities And Its Applications
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher:
Release Date : 1990
Theory Of Singularities And Its Applications written by Vladimir Igorevich Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Singularities (Mathematics) categories.
The theory of singularities lies at the crossroads between those branches of mathematics which are the most abstract and those which are the most applied. Algebraic and differential geometry and topology, commutative algebra and group theory are as intimately connected to singularity theory as are dynamical systems theory, control theory, differential equations, quantum mechanical and quasi-classical asymptotics, optics, and functional analysis. This collection of papers incorporates recent results of participants in the editor's ongoing seminar in singularity theory, held in the Mechanics and.