In a series of papers ([2, 3, 4]) the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. These relations were called in [4] Stationary-to-Randers Correspondence (SRC). In this paper we focus on one aspect of SRC, the equality between the index of a geodesic in a Randers space and that...

Let $$(X,\omega )$$ be a Kähler manifold and $$\psi : \mathbb R \rightarrow R_+$$ concave weight. We show that $${\mathcal {H}}_\omega $$ admits natural metric $$d_\psi whose completion is the low energy space {E}}_\psi , introduced by Guedj–Zeriahi. As not induced Finsler metric, main difficulty to triangle inequality holds. study properties of resulting complete $$({\mathcal ,d_\psi .

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, i.e., at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point...

The global holomorphic invariant αG(X) introduced by Tian [?], Tian and Yau [?] is closely related to the existence of Kähler-Einstein metrics. In his solution to the Calabi conjecture, Yau [?] proved the existence of a Kähler-Einstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is posi...

Abstract In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these by warped product. Using the obtained equations, manufacture new product vanishing These contain metric introduced Berwald and spherically symmetric given Mo-Zhu.

In this paper, we establish a closer relation between the Berwald scalar curvature and [Formula: see text]-curvature. fact, prove that Finsler metric has isotropic if only it weakly For metrics of flag text]-curvature, they have almost text]-curvature is isotropic.

We define bilinear functionals of vector fields and differential forms, the densities which yield metric Einstein tensors on even-dimensional Riemannian manifolds. generalise these concepts in non-commutative geometry and, particular, we prove that for conformally rescaled noncommutative two-torus functional vanishes.