alexa Homogeneous spaces with inner metric and with integrable invariant distributions


Journal of Generalized Lie Theory and Applications

Author(s): V N Berestovskii, V V Gorbatsevich

Abstract Share this page

This paper is a survey of results (partly obtained by the authors) on homogeneous spaces of Lie groups G with a compact stabilizer subgroup H, on which every G-invariant distribution is integrable. It is proved that the condition of integrability is necessary and sufficient for every invariant inner metric to be (holonomic) Finsler on such a space. As a corollary of the obtained results, we assert that the class of homogeneous spaces with invariant non-holonomic Riemannian metrics (in other terms, sub-Riemannian or Carnot–Carathéodory metrics), which were actively studied last 3 decades after Gromov’s work, is rather broad.

This article was published in Analysis and Mathematical Physics and referenced in Journal of Generalized Lie Theory and Applications

Relevant Expert PPTs

Recommended Conferences

Relevant Topics

Peer Reviewed Journals
Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals
International Conferences 2017-18
Meet Inspiring Speakers and Experts at our 3000+ Global Annual Meetings

Contact Us

© 2008-2017 OMICS International - Open Access Publisher. Best viewed in Mozilla Firefox | Google Chrome | Above IE 7.0 version