# Riemannian geometry: (Record no. 6830)

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000 -LEADER | |
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fixed length control field | 04534cam a22005535i 4500 |

001 - CONTROL NUMBER | |

control field | 11319450 |

003 - CONTROL NUMBER IDENTIFIER | |

control field | OSt |

005 - DATE AND TIME OF LATEST TRANSACTION | |

control field | 20160920171744.0 |

006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |

fixed length control field | m d |

007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |

fixed length control field | cr n |

008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |

fixed length control field | 121227s1987 gw | s |||| 0|eng d |

020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |

International Standard Book Number | 9783540204930 (Pbk) |

Terms of availability | Euro 16.99 |

024 7# - OTHER STANDARD IDENTIFIER | |

Standard number or code | 10.1007/978-3-642-97026-9 |

Source of number or code | doi |

035 ## - SYSTEM CONTROL NUMBER | |

System control number | (WaSeSS)ssj0001298324 |

040 ## - CATALOGING SOURCE | |

Modifying agency | WaSeSS |

Transcribing agency | IISERB |

050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |

Classification number | QA641-670 |

072 #7 - SUBJECT CATEGORY CODE | |

Subject category code | PBMP |

Source | bicssc |

072 #7 - SUBJECT CATEGORY CODE | |

Subject category code | MAT012030 |

Source | bisacsh |

082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |

Classification number | 516.36 G138R3 |

Edition number | 23 |

100 1# - MAIN ENTRY--PERSONAL NAME | |

Personal name | Gallot, Sylvestre. |

9 (RLIN) | 5537 |

210 10 - ABBREVIATED TITLE | |

Abbreviated title | Riemannian Geometry |

222 ## - KEY TITLE | |

Key title | Mathematics Collection |

245 10 - TITLE STATEMENT | |

Title | Riemannian geometry: |

Statement of responsibility, etc | by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine. |

250 ## - EDITION STATEMENT | |

Edition statement | 3rd |

260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |

Place of publication, distribution, etc | Heidelberg: |

Name of publisher, distributor, etc | Springer, |

Date of publication, distribution, etc | 2004. |

300 ## - PHYSICAL DESCRIPTION | |

Extent | xv, 322p. |

490 1# - SERIES STATEMENT | |

Series statement | Universitext, |

International Standard Serial Number | 0172-5939 |

505 0# - FORMATTED CONTENTS NOTE | |

Formatted contents note | I: Differential Manifolds -- A. from Submanifolds to Abstract Manifolds -- B. Tangent Bundle -- C. Vector Fields: -- D. Baby lie Groups -- E. Covering maps and Fibrations -- F. Tensors -- G. Exterior forms -- H. Appendix: Partitions of Unity -- II: Riemannian Metrics -- A. Existence Theorems and first Examples -- B. Covariant Derivative -- C. Geodesics -- III: Curvature -- A. the Curvature Tensor -- B. first Second Variation of arc-Length and Energy -- C. Jacobi Vector Fields -- D. Riemannian Submersions and Curvature -- E. The Behavior of Length and Energy in the Neighborhood of a Geodesic -- F. Manifolds with Constant Sectional Curvature -- G. Topology and Curvature -- H. Curvature and Volume -- I. Curvature and Growth of the Fundamental Group -- J. Curvature and Topology -- K. Curvature and Representations of the Orthogonal Group -- Chapitre IV: Analysis on Manifolds and the Ricci Curvature -- A. Manifolds with Boundary -- B. Bishop's Inequality Revisited -- C. Differential forms and Cohomology -- D. Basic Spectral Geometry -- E. Some Examples of Spectra -- F. The Minimax Principle -- V. Riemannian Submanifolds. |

506 ## - RESTRICTIONS ON ACCESS NOTE | |

Terms governing access | License restrictions may limit access. |

520 ## - SUMMARY, ETC. | |

Summary, etc | Traditional point of view: pinched manifolds 147 Almost flat pinching 148 Coarse point of view: compactness theorems of Gromov and Cheeger 149 K. CURVATURE AND REPRESENTATIONS OF THE ORTHOGONAL GROUP Decomposition of the space of curvature tensors 150 Conformally flat manifolds 153 The second Bianchi identity 154 CHAPITRE IV : ANALYSIS ON MANIFOLDS AND THE RICCI CURVATURE A. MANIFOLDS WITH BOUNDARY Definition 155 The Stokes theorem and integration by parts 156 B. BISHOP'S INEQUALITY REVISITED 159 Some commutations formulas Laplacian of the distance function 160 Another proof of Bishop's inequality 161 The Heintze-Karcher inequality 162 C. DIFFERENTIAL FORMS AND COHOMOLOGY The de Rham complex 164 Differential operators and their formal adjoints 165 The Hodge-de Rham theorem 167 A second visit to the Bochner method 168 D. BASIC SPECTRAL GEOMETRY 170 The Laplace operator and the wave equation Statement of the basic results on the spectrum 172 E. SOME EXAMPLES OF SPECTRA 172 Introduction The spectrum of flat tori 174 175 Spectrum of (sn, can) F. THE MINIMAX PRINCIPLE 177 The basic statements VIII G. THE RICCI CURVATURE AND EIGENVALUES ESTIMATES Introduction 181 Bishop's inequality and coarse estimates 181 Some consequences of Bishop's theorem 182 Lower bounds for the first eigenvalue 184 CHAPTER V : RIEMANNIAN SUBMANIFOLDS A. CURVATURE OF SUBMANIFOLDS Introduction 185 Second fundamental form 185 Curvature of hypersurfaces 187 Application to explicit computations of curvature 189 B. CURVATURE AND CONVEXITY 192 The Hadamard theorem C. |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Mathematics. |

9 (RLIN) | 5538 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Global differential geometry. |

9 (RLIN) | 5539 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Cell aggregation |

General subdivision | Mathematics. |

9 (RLIN) | 5540 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Mathematical physics. |

9 (RLIN) | 5541 |

650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Mathematics. |

9 (RLIN) | 5538 |

650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Differential Geometry. |

9 (RLIN) | 5542 |

650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Manifolds and Cell Complexes (incl. Diff.Topology). |

9 (RLIN) | 5543 |

650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Mathematical Methods in Physics. |

9 (RLIN) | 5544 |

650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Numerical and Computational Physics. |

9 (RLIN) | 5545 |

700 1# - ADDED ENTRY--PERSONAL NAME | |

Personal name | Hulin, Dominique. |

9 (RLIN) | 5546 |

700 1# - ADDED ENTRY--PERSONAL NAME | |

Personal name | Lafontaine, Jacques. |

9 (RLIN) | 5547 |

773 0# - HOST ITEM ENTRY | |

Title | Springer eBooks |

773 #0 - HOST ITEM ENTRY | |

Title | SpringerLink ebooks - Mathematics and Statistics (Archive) |

776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |

Display text | Printed edition: |

International Standard Book Number | 9783540179238 |

830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |

Uniform title | Universitext, |

9 (RLIN) | 5549 |

856 40 - ELECTRONIC LOCATION AND ACCESS | |

Public note | Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive) |

910 ## - USER-OPTION DATA (OCLC) | |

User-option data | Vendor-generated brief record |

942 ## - ADDED ENTRY ELEMENTS (KOHA) | |

Source of classification or shelving scheme | |

Koha item type | Books |

Permanent Location | Cost, replacement price | Total Renewals | Date acquired | Koha item type | Current Location | Source of classification or shelving scheme | Damaged status | Barcode | Public note | Price effective from | Withdrawn status | Date last seen | Lost status | Total Checkouts | Date checked out | Shelving location | Full call number | Cost, normal purchase price | Source of acquisition | Not for loan |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Central Library, IISER Bhopal | 1287.84 | 3 | 2015-08-19 | Books | Central Library, IISER Bhopal | 6998 | Reserve | 2015-08-19 | 2023-08-01 | 10 | 2023-08-01 | General Section | 516.36 G138R3 | 1030.27 | 31 | Not For Loan |