Vertical Laplacian on Complex Finsler Bundles
نویسنده
چکیده
In this paper we define vertical and horizontal Laplace type operators for functions on the total space of a complex Finsler bundle (E, L). We also define the ′′ v-Laplacian for (p, q, r, s)-forms with compact support on E and we get the local expression of this Laplacian explicitly in terms of vertical covariant derivatives with respect to the Chern-Finsler linear connection of (E, L).
منابع مشابه
The 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 کاملHorizontal Forms of Chern Type on Complex Finsler Bundles
The aim of this paper is to construct horizontal Chern forms of a holomorphic vector bundle using complex Finsler structures. Also, some properties of these forms are studied.
متن کاملACTA UNIVERSITATIS APULENSIS No 18/2009 ON VECTOR-BUNDLE VALUED COHOMOLOGY ON COMPLEX FINSLER MANIFOLDS
In this paper we define a complex adapted connection of type Bott on vertical bundle of a complex Finsler manifold. When this connection is flat we get a vertical vector valued cohomology. The notions are introduced by analogy with the real case for foliations. Finally, using the partial Bott connection we give a characterization of strongly Kähler-Finsler manifolds. 2000 Mathematics Subject Cl...
متن کاملA Nakano type inequality for mixed forms on complex Finsler manifolds
In this paper, we obtain a Nakano type inequality for vertical valued ∂h harmonic mixed forms with compact support on the total space of the holomorphic tangent bundle of a complex Finsler manifold. AMS subject classifications: 53B40, 32L20
متن کاملThe p - Laplace eigenvalue problem as p → 1 and Cheeger sets in a Finsler metric ∗
We consider the p–Laplacian operator on a domain equipped with a Finsler metric. After deriving and recalling relevant properties of its first eigenfunction for p > 1, we investigate the limit problem as p → 1.
متن کامل