Jacobi-Type Vector Fields on Kaehler Manifold
نویسنده
چکیده
In this paper, we use the notion of Jacobi-type vector fields introduced in [5] to obtain a necessary and sufficient condition for a Kaehler manifold to be isometric to the complex space form (Cn, J, 〈, 〉), where J is the complex structure and 〈, 〉 is the Euclidean metric on Cn. Mathematics Subject Classification: 53C20, 53B21
منابع مشابه
Tangent Bundle of the Hypersurfaces in a Euclidean Space
Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...
متن کاملSome vector fields on a riemannian manifold with semi-symmetric metric connection
In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.
متن کاملThe Hermitian Connection and the Jacobi Fields of a Complex Finsler Manifold
It is proved that all invariant functions of a complex Finsler manifold can be totally recovered from the torsion and curvature of the connection introduced by Kobayashi for holomorphic vector bundles with complex Finsler structures. Equations of the geodesics and Jacobi fields of a generic complex Finsler manifold, expressed by means Kobayashi’s connection, are also derived.
متن کاملIsomorphisms of the Jacobi and Poisson Brackets
We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as for example those given by Poisson or contact structures, but we consider degenerate structures as well. Introduction We shall admit different classes of smoothness, so by a manifold of ...
متن کاملF eb 2 00 1 PARABOLIC VECTOR BUNDLES AND EQUIVARIANT VECTOR BUNDLES
Given a complex manifold X, a normal crossing divisor D ⊂ X whose irreducible components D 1 ,. .. , D s are smooth, and a choice of natural numbers r = (r 1 ,. .. , r s), we construct a manifold X(D, r) with an action of a torus Γ and we prove that some full subcategory of the category of Γ-equivariant vector bundles on X(D, r) is equivalent to the category of parabolic vector bundles on (X, D...
متن کامل