Differential Geometry From A Singularity Theory Viewpoint
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Author | : Shyuichi Izumiya |
Publisher | : World Scientific |
Total Pages | : 383 |
Release | : 2015-10-29 |
Genre | : Mathematics |
ISBN | : 9814590460 |
Download Differential Geometry From A Singularity Theory Viewpoint Book in PDF, Epub and Kindle
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.
Author | : Masaaki Umehara |
Publisher | : |
Total Pages | : 387 |
Release | : 2021 |
Genre | : Curves on surfaces |
ISBN | : 9789811237140 |
Download Differential Geometry Of Curves And Surfaces With Singularities Book in PDF, Epub and Kindle
"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"--
Author | : Shyuichi E. T. Al IZUMIYA |
Publisher | : World Scientific |
Total Pages | : 383 |
Release | : 2015-10-29 |
Genre | : Mathematics |
ISBN | : 9814590452 |
Download Differential Geometry from a Singularity Theory Viewpoint Book in PDF, Epub and Kindle
"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."--
Author | : Shyuichi Izumiya |
Publisher | : |
Total Pages | : |
Release | : 2005 |
Genre | : |
ISBN | : |
Download Differential Geometry from the Viewpoint of Lagrangian Or Legendrian Singularity Theory Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 26 |
Release | : 2005 |
Genre | : |
ISBN | : |
Download Differential Geometry from the Viewpoint of Lagrangian Or Legendrian Singularity Theory Book in PDF, Epub and Kindle
Author | : Masaaki Umehara |
Publisher | : World Scientific |
Total Pages | : 387 |
Release | : 2021-11-29 |
Genre | : Mathematics |
ISBN | : 9811237158 |
Download Differential Geometry Of Curves And Surfaces With Singularities Book in PDF, Epub and Kindle
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.
Author | : J. W. Bruce |
Publisher | : Cambridge University Press |
Total Pages | : 340 |
Release | : 1992-11-26 |
Genre | : Mathematics |
ISBN | : 9780521419857 |
Download Curves and Singularities Book in PDF, Epub and Kindle
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.
Author | : Felipe Cano |
Publisher | : Springer Nature |
Total Pages | : 500 |
Release | : |
Genre | : |
ISBN | : 3031541723 |
Download Handbook of Geometry and Topology of Singularities VI: Foliations Book in PDF, Epub and Kindle
Author | : Jean Pierre Bourguignon |
Publisher | : Cambridge University Press |
Total Pages | : 198 |
Release | : 1998-05-28 |
Genre | : Mathematics |
ISBN | : 9780521632461 |
Download Geometric Theory of Singular Phenomena in Partial Differential Equations Book in PDF, Epub and Kindle
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.
Author | : Masatomo Takahashi |
Publisher | : |
Total Pages | : 125 |
Release | : 2009 |
Genre | : |
ISBN | : |
Download Applications of singularity theory of differential equations and differential geometry Book in PDF, Epub and Kindle