Lectures On The Geometry Of Manifolds (Record no. 59876)
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| 000 -LEADER | |
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| fixed length control field | 02661nam a22001937a 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 230509b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9789811210754 (PB) |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | 514 |
| Item number | NIC |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Nicolaescu, Liviu I |
| 245 ## - TITLE STATEMENT | |
| Title | Lectures On The Geometry Of Manifolds |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 3 |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Singapore |
| Name of publisher | World Scientific |
| Year of publication | 2020 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xviii, 682 p |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro<br/>Contents<br/>Preface<br/>1. Manifolds<br/>1.1 Preliminaries<br/>1.1.1 Space and Coordinatization<br/>1.1.2 The implicit function theorem<br/>1.2 Smooth manifolds<br/>1.2.1 Basic definitions<br/>1.2.2 Partitions of unity<br/>1.2.3 Examples<br/>1.2.4 How many manifolds are there?<br/>2. Natural Constructions on Manifolds<br/>2.1 The tangent bundle<br/>2.1.1 Tangent spaces<br/>2.1.2 The tangent bundle<br/>2.1.3 Transversality<br/>2.1.4 Vector bundles<br/>2.1.5 Some examples of vector bundles<br/>2.2 A linear algebra interlude<br/>2.2.1 Tensor products<br/>2.2.2 Symmetric and skew-symmetric tensors 3.3.6 Connections on tangent bundles<br/>3.4 Integration on manifolds<br/>3.4.1 Integration of 1-densities<br/>3.4.2 Orientability and integration of differential forms<br/>3.4.3 Stokes' formula<br/>3.4.4 Representations and characters of compact Lie groups<br/>3.4.5 Fibered calculus<br/>4. Riemannian Geometry<br/>4.1 Metric properties<br/>4.1.1 Definitions and examples<br/>4.1.2 The Levi-Civita connection<br/>4.1.3 The exponential map and normal coordinates<br/>4.1.4 The length minimizing property of geodesics<br/>4.1.5 Calculus on Riemann manifolds<br/>4.2 The Riemann curvature 4.2.1 Definitions and properties<br/>4.2.2 Examples<br/>4.2.3 Cartan's moving frame method<br/>4.2.4 The geometry of submanifolds<br/>4.2.5 Correlators and their geometry<br/>4.2.6 The Gauss-Bonnet theorem for oriented surfaces<br/>5. Elements of the Calculus of Variations<br/>5.1 The least action principle<br/>5.1.1 The 1-dimensional Euler-Lagrange equations<br/>5.1.2 Noether's conservation principle<br/>5.2 The variational theory of geodesics<br/>5.2.1 Variational formulæ<br/>5.2.2 Jacobi fields<br/>5.2.3 The Hamilton-Jacobi equations<br/>6. The Fundamental Group and Covering Spaces 6.1 The fundamental group<br/>6.1.1 Basic notions<br/>6.1.2 Of categories and functors<br/>6.2 Covering Spaces<br/>6.2.1 Definitions and examples<br/>6.2.2 Unique lifting property<br/>6.2.3 Homotopy lifting property<br/>6.2.4 On the existence of lifts<br/>6.2.5 The universal cover and the fundamental group<br/>7. Cohomology<br/>7.1 DeRham cohomology<br/>7.1.1 Speculations around the Poincaré lemma<br/>7.1.2 Čech vs. DeRham<br/>7.1.3 Very little homological algebra<br/>7.1.4 Functorial properties of the DeRham cohomology<br/>7.1.5 Some simple examples<br/>7.1.6 The Mayer-Vietoris principle |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometry |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Topical term or geographic name as entry element | Mathematics |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | BOOKS |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Full call number | Accession Number | Koha item type | Owner (If the Item is Gratis) | Copy number |
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| IMSc Library | IMSc Library | Multiple Copies Section, Shelf No: 4 | 514 NIC | 77068 | BOOKS | Gratis by NBHM (National Board of Higer Mathematics) | |||||
| IMSc Library | IMSc Library | Multiple Copies Section, Shelf No: 4 | 514 NIC | 77312 | BOOKS | Gratis by NBHM (National Board of Higer Mathematics) | 1 |