regarding the kähler-einstein structure on cartan spaces with berwald connection

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

Ricci Flow on Kähler-einstein Surfaces

Cartan and Berwald Connections in the Pullback Formalism

Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonlinear connection associated with a given regular connection, in the pullback bundle, ...

Einstein–cartan Theory

Standard notation and terminology of differential geometry and general relativity are used in this article. All considerations are local so that the four-dimensional space-time M is assumed to be a smooth manifold diffeomorphic to R4. It is endowed with a metric tensor g of signature (1, 3) and a linear connection defining the covariant differentiation of tensor fields. Greek indices range from...

Kähler-Einstein fillings

We show that on an open bounded smooth strongly pseudoconvex subset of C, there exists a Kähler-Einstein metric with positive Einstein constant, such that the metric restricted to the Levi distribution of the boundary is conformal to the Levi form. To achieve this, we solve an associated complex Monge-Ampère equation with Dirichlet boundary condition. We also prove uniqueness under some more as...

Homogeneous Para - Kähler Einstein

A para-Kähler manifold can be defined as a pseudoRiemannian manifold (M, g) with a parallel skew-symmetric paracomplex structures K, i.e. a parallel field of skew-symmetric endomorphisms with K = Id or, equivalently, as a symplectic manifold (M, ω) with a bi-Lagrangian structure L, i.e. two complementary integrable Lagrangian distributions. A homogeneous manifold M = G/H of a semisimple Lie gro...