LICHNEROWICZ CONNECTIONS IN ALMOST COMPLEX FINSLER MANIFOLDS

Abstract

We consider the connections <TEX>$\nabla$</TEX> on the Rizza manifold (M, J, L) satisfying <TEX>${\nabla}G=0\;and\;{\nabla}J=0$</TEX>. Among them, we derive a Lichnerowicz connection from the Cart an connection and characterize it in terms of torsion. Generalizing Kahler condition in Hermitian geometry, we define a Kahler condition for Rizza manifolds. For such manifolds, we show that the Cartan connection and the Lichnerowicz connection coincide and that the almost complex structure J is integrable.