Isometric action of SL(2,R) on homogeneous spaces

Autor:	Kisil, Anastasia V.
Rok vydání:	2008
Předmět:	Mathematics - Metric Geometry Mathematics - Complex Variables Mathematics - Differential Geometry 32F45 30F45 51K05 53C22
Zdroj:	Adv. App. Clifford Algebras 20 (2010), no. 2, 299-312
Druh dokumentu:	Working Paper
DOI:	10.1007/s00006-010-0203-2
Popis:	We investigate the SL(2,R) invariant geodesic curves with the as- sociated invariant distance function in parabolic geometry. Parabolic geom- etry naturally occurs in the study of SL(2,R) and is placed in between the elliptic and the hyperbolic (also known as the Lobachevsky half-plane and 2- dimensional Minkowski half-plane space-time) geometries. Initially we attempt to use standard methods of finding geodesics but they lead to degeneracy in this setup. Instead, by studying closely the two related elliptic and hyperbolic geometries we discover a unified approach to a more exotic and less obvious parabolic case. With aid of common invariants we describe the possible dis- tance functions that turn out to have some unexpected, interesting properties. Comment: LaTeX, 10 pages, 9 EPS figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0810.0368 Zobrazit plný text záznamu View this record from Arxiv