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http://dx.doi.org/10.4134/BKMS.2005.42.2.405

LICHNEROWICZ CONNECTIONS IN ALMOST COMPLEX FINSLER MANIFOLDS  

LEE, NANY (DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF SEOUL)
WON, DAE-YEON (DEPARTMENT OF MATHEMATICS, DUKSUNG WOMEN'S UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.42, no.2, 2005 , pp. 405-413 More about this Journal
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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