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Curvature : a variational approach

Author: Andrei A Agrachev; Davide Barilari; L Rizzi
Publisher: Providence, RI : American Mathematical Society, [2018]
Series: Memoirs of the American Mathematical Society, no. 1225.
Edition/Format:   Print book : EnglishView all editions and formats
Publication:Memoirs of the American Mathematical Society, no:1225
Summary:

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  Read more...

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Document Type: Book
All Authors / Contributors: Andrei A Agrachev; Davide Barilari; L Rizzi
ISBN: 9781470426460 1470426463
OCLC Number: 1048943221
Notes: "November 2018, volume 256, number 1225 (first of 6 numbers)."
Description: v, 142 pages : illustrations ; 26 cm.
Contents: Chapter 1. Introduction Chapter 2. General setting Chapter 3. Flag and growth vector of an admissible curve Chapter 4. Geodesic cost and its asymptotics Chapter 5. Sub-Riemannian geometry Chapter 6. Jacobi curves Chapter 7. Asymptotics of the Jacobi curve: Equiregular case Chapter 8. Sub-Laplacian and Jacobi curves 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 C(t,s) 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 ct.
Series Title: Memoirs of the American Mathematical Society, no. 1225.
Responsibility: A. Agrachev, D. Barilari, L. Rizzi.

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