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Lichnerowicz connections in almost complex Finsler manifolds
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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.
참고문헌 (8)
- "Lecture Notes in Mathematics" (1994), Springer-Verlag
- "{\it An Introduction toRiemannian-Finsler geometry} Grad. Texts in Math. 2000."
- "{\it A relation between Finslerian and Hermitianmetrics}", (s.), pp.1~ (1965)
- "{\it Finsler metrics on almost complex manifolds}", pp.1~, Riv. Mat. Univ. Parma
- "Almost complex manifolds and hyperbolicity", pp.246~ (2001)
- "{\it Natural connections in almost complex manifolds}", pp.175~178 (2003)
- "{\it Connections in almost complex Finslermanifolds and hyperbolicity}" (2004)
- "{\it Foundations of Finsler geometry and specialFinsler spaces}" (1986), Kaiseisha Press
관련 논문AI추천
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