Vector Bundles and Paracontact Finsler Structures

Finsler Geometry of Projectivized Vector Bundles

Some linear Jacobi structures on vector bundles

We study Jacobi structures on the dual bundle A to a vector bundle A such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on A and a 1-cocycle φ ∈ Γ(A) induce a Jacobi structure on A satisfying the above conditions. Moreover, we show that this correspo...

Concurrent vector fields on Finsler spaces

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

Finsler Geometry of Holomorphic Jet Bundles

Introduction 107 1. Holomorphic Jet Bundles 113 2. Chern Classes and Cohomology Groups: The Case of Curves 120 3. Computation of Chern Classes: The Case of Surfaces 139 4. Finsler Geometry of Projectivized Vector Bundles 148 5. Weighted Projective Spaces and Projectivized Jet Bundles 153 6. The Lemma of Logarithmic Derivatives and the Schwarz Lemma 164 7. Surfaces of General Type 173 Acknowledg...

Vertical Laplacian on Complex Finsler Bundles

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).