000			02557nam a22002297a 4500
003			CUTN
005			20230413155015.0
008			230413b |||||||| |||| 00| 0 eng d
020			_a9781944660451
041			_aEnglish
082			_223 _a516.36 _bUME
100			_a Umehara, Masaaki
245			_a Differential geometry of curves and surfaces with singularities / _cMasaaki Umehara1 et.al.
250			_a1st
260			_aSingapore: _bWorld Scientific, _c2022.
300			_axvi, 370 p.: _bill.; _c24 cm.
505			_a1. Planar curves and singular points _t2. Singularities of surfaces _t3. Proofs of criteria for singularities _t4. Applications of criteria for singularities _t5. Singular curvature _t6. Gauss-Bonnet type formulas and applications _t7. Flat surfaces in R³ _t8. Proof of the criterion for swallowtails _t9.Coherent tangent bundles _t10. 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			_a Courbes sur les surfaces, Curves on surfaces
700			_aSaji , Kentarō
942			_2ddc _cBOOKS
999			_c38438 _d38438