Differential Geometry of Curves and Surfaces with Singularities (Record no. 60041)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02654nam a22002657a 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240226b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9781944660451 (PB) |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | 514.7 |
| Item number | UME |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Umehara, Masaaki |
| 245 ## - TITLE STATEMENT | |
| Title | Differential Geometry of Curves and Surfaces with Singularities |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Singapore |
| Name of publisher | World Scientific |
| Year of publication | 2023 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xvi, 370p. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references (pages 361-365) and index |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Planar Curves and Singular Points <br/>2. Singularities of Surfaces <br/>3. Proofs of Criteria for Singularities <br/>4. Applications of Criteria for Singularities <br/>5. Singular Curvature <br/>6. Gauss–Bonnet Type Formulas and Applications <br/>7. Flat Surfaces in R³ <br/>8. Proof of the Criterion for Swallowtails <br/>9. Coherent Tangent Bundles <br/>10. Contact Structure and Wave Fronts |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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.<br/><br/>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.<br/><br/>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.<br/><br/>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 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Division lemma |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Singularity theory |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Differential geometry |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Topical term or geographic name as entry element | Mathematics |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Saji, Kentaro |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Yamada, Kotaro |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Rossman, Wayne (Translator) |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | BOOKS |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Full call number | Accession Number | Copy number | Koha item type | Owner (If the Item is Gratis) | Shelving location |
|---|---|---|---|---|---|---|---|---|---|---|---|
| IMSc Library | IMSc Library | 514.7 UME | 77516 | 1 | BOOKS | NBHM through KNR | |||||
| IMSc Library | IMSc Library | 514.7 UME | 77532 | 2 | BOOKS | NBHM through R. Balasubramanian | Multiple Copies Section |