On the geometry of indicatrix of a complex Finsler space

Abstract

In this note the geometry of the indicatrix is studied as a hypersurface of a complex Finsler space. Relative to the induced frame of the Chern-Finsler complex nonlinear connection we prove the existence of a metrical contact structure on the complexified bundle T_CI of the complex indicatrix. The action of this structure and the induced Chern-Finsler linear connection on T_CI are studied. The circumstances when the contact structure is one normal on T' (T'M) = T_CI ⊗ N, where N is the unit orthogonal vector to the hypersurface, are obtained.