Negative Vector Bundles and Complex Finsler Structures

Finsler Geometry of Projectivized Vector Bundles

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).

Horizontal 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.

Complex Structures on Principal Bundles

Holomorphic principal Gbundles over a complex manifold M can be studied using non-abelian cohomology groups H(M,G). On the other hand, if M = Σ is a closed Riemann surface, there is a correspondence between holomorphic principal G-bundles over Σ and coadjoint orbits in the dual of a central extension of the Lie algebra C∞(Σ, g). We review these results and provide the details of an integrabilit...

Complex Vector Bundles and Jacobi Forms

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi–Yau manifold. In physics such a function appears as the partition function of N = 2 superconformal field theories. In these notes we define the modified ...