In this paper we study the complex indicatrix associated to a complex
Finsler space as an embedded CR - hypersurface of the holomorphic tangent
bundle, considered in a fixed point. Following the study of CR -
submanifolds of a K?hler manifold, there are investigated some properties
of the complex indicatrix as a real submanifold of codimension one, using
the submanifold formulae and the fundamental equations. As a result, the
complex indicatrix is an extrinsic sphere of the holomorphic tangent space
in each fibre of a complex Finsler bundle. Also, submersions from the
complex indicatrix onto an almost Hermitian manifold and some properties
that can occur on them are studied. As application, an explicit submersion
onto the complex projective space is provided.
From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space
