Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions

Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions
Author :
Publisher : American Mathematical Soc.
Total Pages : 121
Release :
ISBN-10 : 9780821804049
ISBN-13 : 0821804049
Rating : 4/5 (49 Downloads)

Book Synopsis Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions by : Wensheng Liu

Download or read book Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions written by Wensheng Liu and published by American Mathematical Soc.. This book was released on 1995 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sub-Riemannian manifold ([italic capitals]M, E, G) consists of a finite-dimensional manifold [italic capital]M, a rank-two bracket generating distribution [italic capital]E on [italic capital]M, and a Riemannian metric [italic capital]G on [italic capital]E. All length-minimizing arcs on ([italic capitals]M, E, G) are either normal extremals or abnormal extremals. Normal extremals are locally optimal, i.e., every sufficiently short piece of such an extremal is a minimizer. The question whether every length-minimizer is a normal extremal was recently settled by R. G. Montgomery, who exhibited a counterexample. The present work proves that regular abnormal extremals are locally optimal, and, in the case that [italic capital]E satisfies a mild additional restriction, the abnormal minimizers are ubiquitous rather than exceptional. All the topics of this research report (historical notes, examples, abnormal extremals, Hamiltonians, nonholonomic distributions, sub-Riemannian distance, the relations between minimality and extremality, regular abnormal extremals, local optimality of regular abnormal extremals, etc.) are presented in a very clear and effective way.


Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions Related Books

Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions
Language: en
Pages: 121
Authors: Wensheng Liu
Categories: Mathematics
Type: BOOK - Published: 1995 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

A sub-Riemannian manifold ([italic capitals]M, E, G) consists of a finite-dimensional manifold [italic capital]M, a rank-two bracket generating distribution [it
Shortest Paths for Sub-Riemannian Metrics on Rank-two Distributions
Language: en
Pages: 104
Authors: Wensheng Liu
Categories: Geodesics
Type: BOOK - Published: 1995 - Publisher:

DOWNLOAD EBOOK

Sub-Riemannian Geometry
Language: en
Pages: 404
Authors: Andre Bellaiche
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

DOWNLOAD EBOOK

Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen y
Sub-Riemannian Geometry
Language: en
Pages: 371
Authors: Ovidiu Calin
Categories: Mathematics
Type: BOOK - Published: 2009-04-20 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.
Geometric Control Theory and Sub-Riemannian Geometry
Language: en
Pages: 385
Authors: Gianna Stefani
Categories: Mathematics
Type: BOOK - Published: 2014-06-05 - Publisher: Springer

DOWNLOAD EBOOK

Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry.