MARC details
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02557nam a22002297a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
CUTN |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20230413155015.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
230413b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781944660451 |
| 041 ## - LANGUAGE CODE |
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| Language |
English |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
23 |
| Classification number |
516.36 |
| Item number |
UME |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Umehara, Masaaki |
| 245 ## - TITLE STATEMENT |
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| Title |
Differential geometry of curves and surfaces with singularities / |
| Statement of responsibility, etc |
Masaaki Umehara1 et.al. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1st |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Singapore: |
| Name of publisher, distributor, etc |
World Scientific, |
| Date of publication, distribution, etc |
2022. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xvi, 370 p.: |
| Other physical details |
ill.; |
| Dimensions |
24 cm. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Contents |
1. Planar curves and singular points<br/> |
| Title |
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. |
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| 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. 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 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Courbes sur les surfaces, Curves on surfaces |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Saji , Kentarō |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
General Books |
