SKOLKOVO Library

SKOLKOVO School of Management

Differential Geometry : (Record no. 4649)

000 -LEADER
fixed length control field 05455cam a22004335i 4500
001 - CONTROL NUMBER
control field 21684310
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220829135511.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION
fixed length control field m |o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr |||||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 170602s2017 gw |||| o |||| 0|eng
010 ## - LIBRARY OF CONGRESS CONTROL NUMBER
LC control number 2019750509
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783319550848
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-3-319-55084-8
Source of number or code doi
035 ## - SYSTEM CONTROL NUMBER
System control number (DE-He213)978-3-319-55084-8
040 ## - CATALOGING SOURCE
Original cataloging agency DLC
Language of cataloging eng
Description conventions pn
-- rda
Transcribing agency DLC
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT012030
Source bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBMP
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBMP
Source thema
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 516.36
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Tu, Loring W.
Relator term author.
245 10 - TITLE STATEMENT
Title Differential Geometry :
Remainder of title Connections, Curvature, and Characteristic Classes /
Statement of responsibility, etc by Loring W. Tu.
250 ## - EDITION STATEMENT
Edition statement 1st ed. 2017.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (XVII, 347 pages 87 illustrations, 15 illustrations in color.)
490 1# - SERIES STATEMENT
Series statement Graduate Texts in Mathematics,
International Standard Serial Number 0072-5285 ;
Volume number/sequential designation 275
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Preface -- Chapter 1. Curvature and Vector Fields -- 1. Riemannian Manifolds -- 2. Curves -- 3. Surfaces in Space -- 4. Directional Derivative in Euclidean Space -- 5. The Shape Operator -- 6. Affine Connections -- 7. Vector Bundles -- 8. Gauss's Theorema Egregium -- 9. Generalizations to Hypersurfaces in Rn+1 -- Chapter 2. Curvature and Differential Forms -- 10. Connections on a Vector Bundle -- 11. Connection, Curvature, and Torsion Forms -- 12. The Theorema Egregium Using Forms -- Chapter 3. Geodesics -- 13. More on Affine Connections -- 14. Geodesics -- 15. Exponential Maps -- 16. Distance and Volume -- 17. The Gauss-Bonnet Theorem -- Chapter 4. Tools from Algebra and Topology -- 18. The Tensor Product and the Dual Module -- 19. The Exterior Power -- 20. Operations on Vector Bundles -- 21. Vector-Valued Forms -- Chapter 5. Vector Bundles and Characteristic Classes -- 22. Connections and Curvature Again -- 23. Characteristic Classes -- 24. Pontrjagin Classes -- 25. The Euler Class and Chern Classes -- 26. Some Applications of Characteristic Classes -- Chapter 6. Principal Bundles and Characteristic Classes -- 27. Principal Bundles -- 28. Connections on a Principal Bundle -- 29. Horizontal Distributions on a Frame Bundle -- 30. Curvature on a Principal Bundle -- 31. Covariant Derivative on a Principal Bundle -- 32. Character Classes of Principal Bundles -- A. Manifolds -- B. Invariant Polynomials -- Hints and Solutions to Selected End-of-Section Problems -- List of Notations -- References -- Index.
520 ## - SUMMARY, ETC.
Summary, etc This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern-Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss-Bonnet theorem. Exercises throughout the book test the reader's understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Algebraic geometry.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Differential geometry.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Differential Geometry.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Algebraic Geometry.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Print version:
Title Differential geometry : connections, curvature, and characteristic classes
International Standard Book Number 9783319550824
Record control number (DLC) 2017935362
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783319550824
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783319550831
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783319855622
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Graduate Texts in Mathematics,
Volume number/sequential designation 275
856 ## - ELECTRONIC LOCATION AND ACCESS
Materials specified Full-text here
Uniform Resource Identifier https://box.skoltech.ru/index.php/apps/files/?dir=/e-books%20library/Differential%20geometry%20%3A%20connections%2C%20curvature%2C%20and%20characteristic%20classes&fileid=8328234#pdfviewer
906 ## - LOCAL DATA ELEMENT F, LDF (RLIN)
a 0
b ibc
c origres
d u
e ncip
f 20
g y-gencatlg
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Koha item type Book
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Permanent Location Current Location Shelving location Date acquired Full call number Date last seen Price effective from Koha item type Total Checkouts Total Renewals Barcode Date checked out
          Skoltech library Skoltech library Shelves 2021-09-10 QA641 T70 2021-09-10 2021-09-10 E-Book        
          Skoltech library Skoltech library Shelves 2021-12-13 QA641 .T70 2023-09-01 2021-12-13 Book 2 5 2000007836 2023-04-05