On the indicatrix of a complex Cartan space

Abstract

In this paper, we study the geometry of the complex indicatrix of a complex Cartan space. We prove that the intrinsic Chern-Cartan complex nonlinear connection of the indicatrix coincides with the induced Chern-Cartan complex nonlinear connection. Also, the induced Chern-Cartan linear connection on the complexified bundle T_C(S*M) of the complex indicatrix is studied and the existence of an almost hermitian contact structure is proved. The notions are introduced in a similar manner to the corresponding results from complex Finsler geometry, see [7, 8].