Lichnerowicz connections in almost complex Finsler manifolds
Bull. Korean Math. Soc. 2005 Vol. 42, No. 2, 405-413
Published online 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.
Keywords : Finsler metric, almost complex manifold, Rizza manifold, Cartan connection, Kahler condition
MSC numbers : Primary 53B40; Secondary 53B35, 32Q60
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