000			02948nam a22003017a 4500
003			LDD
005			20240627063026.0
008			240627b |||||||| |||| 00| 0 eng d
020			_a9781944660451
040			_cIGNOU Library
041			_aEnglish
082			_a516.36 Um2D
100			_aUmehara, Masaaki _eAuthor. _920016
245			_aDifferential geometry of curves and surfaces with singularities / _cMasaaki Umehara, Kentaro Saji and Kotaro Yamada ; translated by Wayne Rossman
260			_aSingapore : _bWorld Scientific, _c2023.
300			_axvi, 370p
440			_aSeries in algebraic and differential geometry ; _nvolume 1 _920017
500			_aGifted by NBHM through School of Science, IGNOU
505			_a1. Planar Curves and Singular Points 2. Singularities of Surfaces 3. Proofs of Criteria for Singularities 4. Applications of Criteria for Singularities 5. Singular Curvature 6. Gauss–Bonnet Type Formulas and Applications 7. Flat Surfaces in R³ 8. Proof of the Criterion for Swallowtails 9. Coherent Tangent Bundles 10. Contact Structure and Wave Fronts
520			_aThis 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.
650			_aGeometry, Differential. _920018
650			_aCurves on surfaces. _920019
650			_aSingularities (Mathematics) _920020
700			_aSaji, Kentarō, _eAuthor _920021
700			_aYamada, Kotaro _d1961- _eAuthor. _920022
700			_aRossman, Wayne, _d1965- _eTranslator. _920023
942			_2ddc _cMP
999			_c199604 _d199604