An adapted frame on the indicatrix bundle of a complex Finsler space

Abstract

Following the study of the indicatrix of a complex Finsler space (M, L) initiated in [10], in this paper, an adapted frame is introduced on the complexified real tangent bundle of the complex Finsler manifold in a manner that makes it easier to study the properties of the indicatrix bundle. The indicatrix IM is studied as a hypersurface of the holomorphic tangent bundle T0M and the adapted frame obtained on it gives simplified expressions of the equations of the subspace. Using them, a link between the curvature and torsion coefficients of the induced tangent connection and the ones existing on the ambient manifold is obtained.