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Differential geometry of curves and surfaces with singularities / Masaaki Umehara, Tokyo Institute of Technology, Japan; Kentaro Saji, Kobe University, Japan; Kotaro Yamada, Tokyo Institute of Technology, Japan ; translated by Wayne Rossman, Kobe University, Japan.

By: Umehara, Masaaki [author.].
Contributor(s): Saji, Kentarō [author.] | Yamada, Kotaro, 1961- [author.] | Rossman, Wayne, 1965- [translator.].
Material type: TextTextSeries: Series in algebraic and differential geometry ; volume 1.Publisher: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2022]Description: xvi, 370 pages : Rs.1395.00 illustrations ; 24 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9789811237133; 9811237131.Uniform titles: Tokuisen wo motsu kyokusen to kyokumen no bibunkikagaku. English Subject(s): Geometry, Differential | Curves on surfaces | Singularities (Mathematics) | Curves on surfaces | Geometry, Differential | Singularities (Mathematics)DDC classification: 516.3/6
Contents:
Planar curves and singular points -- Singularities of surfaces -- Proofs of criteria for singularities -- Applications of criteria for singularities -- Singular curvature -- Gauss-Bonnet type formulas and applications -- Flat surfaces in R³ -- Proof of the criterion for swallowtails -- Coherent tangent bundles -- Contact structure and wave fronts.
Summary: "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"-- Provided by publisher.
List(s) this item appears in: 2023-09-29
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		516.36 UME (Browse shelf) Available 11100
Total holds: 0

Originally published in Japan in 2017 by Maruzen Publishing Co., Ltd, as Tokuisen Wo Motsu Kyokusen To Kyokumen No Bibunkikagaku.

Includes bibliographical references and index.

Planar curves and singular points -- Singularities of surfaces -- Proofs of criteria for singularities -- Applications of criteria for singularities -- Singular curvature -- Gauss-Bonnet type formulas and applications -- Flat surfaces in R³ -- Proof of the criterion for swallowtails -- Coherent tangent bundles -- Contact structure and wave fronts.

"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"-- Provided by publisher.