Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8705Complete Foliations with Transverse Rigid Geometries and Their Basic AutomorphismsZhukovaN IКафедра математики и механики; Нижегородский государственный университет им. Н.И. Лобачевского; Nizhny Novgorod State University-Nizhny Novgorod State University150220092143508092016Copyright © 2009,2009The notion of rigid geometry is introduced. Rigid geometries include Cartan geometries as
well as rigid geometric structures in the sense of Gromov. Foliations with transverse
rigid geometries are investigated. An invariant g0 of a foliation with transverse rigid
geometry, being a Lie algebra, is introduced. We prove that if, for some foliation with
transverse rigid geometry, g0 is zero, then there exists a unique Lie group structure on its full
basic automorphism group. Some estimates of the dimensions of this group depending on the
transverse geometry are obtained. Examples, illustrating the main results, are constructed.rigid geometryfoliationbasic automorphismholonomy group