Differential Geometry Of Curves And Surfaces With Singularities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry Of Curves And Surfaces With Singularities write by Masaaki Umehara. This book was released on 2021. Differential Geometry Of Curves And Surfaces With Singularities available 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"--
Differential Geometry Curves Surfaces
Differential Geometry Curves Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry Curves Surfaces write by . This book was released on 2021-12-20. Differential Geometry Curves Surfaces available in PDF, EPUB and Kindle.
Differential Geometry Of Curves And Surfaces With Singularities
Differential Geometry Of Curves And Surfaces With Singularities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry Of Curves And Surfaces With Singularities write by Masaaki Umehara. This book was released on 2021-11-29. Differential Geometry Of Curves And Surfaces With Singularities available 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.
The Classical Differential Geometry of Curves and Surfaces
The Classical Differential Geometry of Curves and Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Classical Differential Geometry of Curves and Surfaces write by Georges Valiron. This book was released on 1986. The Classical Differential Geometry of Curves and Surfaces available in PDF, EPUB and Kindle.
Differential Geometry Of Curves And Surfaces
Differential Geometry Of Curves And Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry Of Curves And Surfaces write by Masaaki Umehara. This book was released on 2017-05-12. Differential Geometry Of Curves And Surfaces available in PDF, EPUB and Kindle. 'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.
