Geodesics on the Indicatrix of a Complex Finsler Manifold
نویسندگان
چکیده
In this note the geometry of the indicatrix (I, L̃) is studied as a hypersurface of a complex Finsler space (M,L). The induced Chern-Finsler and Berwald connections are defined and studied. The induced Berwald connection coincides with the intrinsic Berwald connection of the indicatrix bundle. We considered a special projection of a geodesic curve on a complex Finsler space (M,L), called the induced complex geodesic, and a complex geodesic curve on the indicatrix (I, L̃) obtained by using the variational problem for their horizontal lift to TC(T ′M). Then we determined the circumstances in which the induced geodesic coincides with the complex geodesic on the indicatrix. If (M,L) is a weakly Kähler Finsler space, then one condition for these curves to coincide is that the weakly Kähler character conveys to the indicatrix via the induced Chern-Finsler connection. 2000 Mathematics Subject Classification: 53B40.
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