Lichnerowicz connections in almost complex Finsler manifolds
Bull. Korean Math. Soc. 2005 Vol. 42, No. 2, 405-413 Printed June 1, 2005
Nany Lee and Dae Yeon Won The University of Seoul, Duksung Women's University
Abstract : We consider the connections $\nabla \/$ on the Rizza manifold $(M,J,L)\/$ satisfying $\nabla G=0\/$ and $\nabla J=0\/.$ Among them, we derive a Lichnerowicz connection from the Cartan connection and characterize it in terms of torsion. Generalizing K\"ahler condition in Hermitian geometry, we define a K\"ahler 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.