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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)
  • Published : 2005.05.01

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

References

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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