Equality of hh -curvatures of the Berwald and Cartan connections leads to a new class of Finsler metrics, socalled BC-generalized Landsberg metrics. Here, we prove that every BC-generalized Landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

A known general program, designed to endow the quotient space U / B of unitary groups , C ∗ algebras ⊂ with an invariant Finsler metric, is applied obtain a metric for I ( H ) partial isometries Hilbert . group × where algebra bounded linear operators in Under this solution best approximation problem leads computation minimal geodesics space. We find solutions problem, and study properties obta...

The paper establishes that a generalization of Monge–Kantorovich equation gives rise to necessary and sufficient optimality condition for the Kantorovich dual problem minimal flow associated with very degenerate Finsler metric without any assumption on coerciveness.

In this paper, we show that the analogue of Thurston's asymmetric metric on Teichmüller space flat structures torus is weak Finsler and give a geometric description its unit circle at each point in tangent to space. We then introduce family metrics which interpolate between (which coincides with hyperbolic metric). describe circles family.

In this note, we prove the Morse index theorem for a geodesic connecting two submanifolds in $$C^7$$ manifold with $$C^6$$ (conic) pseudo-Finsler metric provided that fundamental tensor is positive definite along velocity curve of geodesic.

In this paper we parallelly build up the theories of normed linear spaces and of linear spaces with indefinite metric, called also Minkowski spaces for finite dimensions in the literature. In the first part of this paper we collect the common properties of the semi-and indefinite-inner-products and define the semi-indefinite-inner-product and the corresponding structure, the semi-indefinite-inn...

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 .