ORPP logo

Curvature : (Record no. 7632)

MARC details
000 -LEADER
fixed length control field 05206nam a22005053i 4500
001 - CONTROL NUMBER
control field EBC5633662
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240724113522.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2019 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470449131
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781470426460
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC5633662
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL5633662
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1083462573
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA645 .A373 2018
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 516.362
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Agrachev, A.
245 10 - TITLE STATEMENT
Title Curvature :
Remainder of title a Variational Approach.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 2019.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2018.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (154 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Memoirs of the American Mathematical Society Series ;
Volume/sequential designation v.256
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title page -- Chapter 1. Introduction -- 1.1. Structure of the paper -- 1.2. Statements of the main theorems -- 1.3. The Heisenberg group -- Part 1 . Statements of the results -- Chapter 2. General setting -- 2.1. Affine control systems -- 2.2. End-point map -- 2.3. Lagrange multipliers rule -- 2.4. Pontryagin Maximum Principle -- 2.5. Regularity of the value function -- Chapter 3. Flag and growth vector of an admissible curve -- 3.1. Growth vector of an admissible curve -- 3.2. Linearised control system and growth vector -- 3.3. State-feedback invariance of the flag of an admissible curve -- 3.4. An alternative definition -- Chapter 4. Geodesic cost and its asymptotics -- 4.1. Motivation: a Riemannian interlude -- 4.2. Geodesic cost -- 4.3. Hamiltonian inner product -- 4.4. Asymptotics of the geodesic cost function and curvature -- 4.5. Examples -- Chapter 5. Sub-Riemannian geometry -- 5.1. Basic definitions -- 5.2. Existence of ample geodesics -- 5.3. Reparametrization and homogeneity of the curvature operator -- 5.4. Asymptotics of the sub-Laplacian of the geodesic cost -- 5.5. Equiregular distributions -- 5.6. Geodesic dimension and sub-Riemannian homotheties -- 5.7. Heisenberg group -- 5.8. On the "meaning" of constant curvature -- Part 2 . Technical tools and proofs -- Chapter 6. Jacobi curves -- 6.1. Curves in the Lagrange Grassmannian -- 6.2. The Jacobi curve and the second differential of the geodesic cost -- 6.3. The Jacobi curve and the Hamiltonian inner product -- 6.4. Proof of Theorem -- 6.5. Proof of Theorem -- Chapter 7. Asymptotics of the Jacobi curve: Equiregular case -- 7.1. The canonical frame -- 7.2. Main result -- 7.3. Proof of Theorem 7.4 -- 7.4. Proof of Theorem -- 7.5. A worked out example: 3D contact sub-Riemannian structures -- Chapter 8. Sub-Laplacian and Jacobi curves -- 8.1. Coordinate lift of a local frame.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 8.2. Sub-Laplacian of the geodesic cost -- 8.3. Proof of Theorem -- Part 3 . Appendix -- Appendix A. Smoothness of value function (Theorem 2.19) -- Appendix B. Convergence of approximating Hamiltonian systems (Proposition 5.15) -- Appendix C. Invariance of geodesic growth vector by dilations (Lemma 5.20) -- Appendix D. Regularity of ( , ) for the Heisenberg group (Proposition 5.51) -- Appendix E. Basics on curves in Grassmannians (Lemma 3.5 and 6.5) -- Appendix F. Normal conditions for the canonical frame -- Appendix G. Coordinate representation of flat, rank 1 Jacobi curves (Proposition 7.7) -- Appendix H. A binomial identity (Lemma 7.8) -- Appendix I. A geometrical interpretation of _{ } -- Bibliography -- Index -- Back Cover.
520 ## - SUMMARY, ETC.
Summary, etc. The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot-Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Curvature.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Riemannian manifolds.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Geometry, Differential.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Barilari, D.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Rizzi, L.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Agrachev, A.
Title Curvature: a Variational Approach
Place, publisher, and date of publication Providence : American Mathematical Society,c2019
International Standard Book Number 9781470426460
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Memoirs of the American Mathematical Society Series
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5633662">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5633662</a>
Public note Click to View

No items available.

© 2024 Resource Centre. All rights reserved.