104 research outputs found

    Looking for K\"ahler- Einstein Structure on Cartan Spaces with Berwald connection

    Full text link
    A Cartan manifold is a smooth manifold M whose slit cotangent bundle T*M0 is endowed with a regular Hamiltonian K which is positively homogeneous of degree 2 in momenta. The Hamiltonian K defines a (pseudo)-Riemannian metric gij in the vertical bundle over T*M0 and using it a Sasaki type metric on T*M0 is constructed. A natural almost complex structure is also defined by K on T*M0 in such a way that pairing it with the Sasaki type metric an almost K\"ahler structure is obtained. In this paper we deform gij to a pseudo-Riemannian metric Gij and we define a corresponding almost complex K\"ahler structure. We determine the Levi-Civita connection of G and compute all the components of its curvature. Then we prove that if the structure (T*M0, G, J) is K\"ahler- Einstein, then the Cartan structure given by K reduce to a Riemannian one.Comment: This article is in 15 page. arXiv admin note: text overlap with this http URL and arXiv:1202.6202 by other autho

    Almost Paracontact Finsler Structures on Vector Bundle

    Full text link
    In this paper, we define almost paracontact and normal almost paracontact Finsler structures on a vector bundle and find some conditions for integrability of these structures. We define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracontact Finsler structure, we find the vertical and horizontal flag curvatures. Then, we define vertical ?-flag curvature and prove that every locally symmetric para-Sasakian Finsler structure has negative vertical ?-flag curvature. Finally, we define the horizontal and vertical Ricci tensors of a para-Sasakian Finsler structure and study some curvature properties of them
    • …
    corecore