Complex Finsler vector bundles with positive Kobayashi curvature

Finsler Geometry of Projectivized Vector Bundles

Nonreversible Finsler Metrics of Positive Flag Curvature

Vector Bundles, Connections and Curvature

Definition 1. Let M be a differentiable manifold. A C∞ complex vector bundle consists of a family {Ex}x∈M of complex vector spaces parametrized by M , together with a C∞ manifold structure of E = ∪x∈MEx such that 1. The projection map π : E →M taking Ex to x is C∞, and 2. For every x0 ∈M , there exists an open set U inM containing x0 and a diffeomorphism φU : π −1(U)→ U × C taking a vector spac...

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).

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...