# LICHNEROWICZ CONNECTIONS IN ALMOST COMPLEX FINSLER MANIFOLDS

• Published : 2005.05.01
• 92 2

#### 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 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.

#### Keywords

Finsler metric;almost complex manifold;Rizza manifold;Cartan connection;Kahler condition

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#### Cited by

1. An almost paracontact structure on a Rizza manifold vol.349, pp.11-12, 2011, https://doi.org/10.1016/j.crma.2011.06.005