In this paper we investigate the spectral problem in Finsler geometry. Due to nonlinearity of Finsler–Laplacian operator, introduce faithful dimension pairs by means which spectrum a compact reversible metric measure manifold is defined. Various upper and lower bounds such eigenvalues are provided spirit Cheng, Buser Gromov, extend several aspects results Hassannezhad, Kokarev Polterovich. More...

A Finsler manifold is said to be geodesically reversible if the reversed curve of any geodesic remains a geometrical geodesic. Well-known examples metrics are Randers with closed [Formula: see text]-forms. Another family well-known projectively flat on text]-sphere that have constant positive curvature. In this paper, we prove some and dynamical characterizations metrics, several rigidity resul...

In this paper, we first establish several theorems about the estimation of distance function on real and strongly convex complex Finsler manifolds then obtain a Schwarz lemma from weakly K\"ahler-Finsler manifold into pseudoconvex manifold. As applications, prove that holomorphic mapping is necessary constant under an extra condition. particular, Minkowski space such its sectional curvature bou...

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo–Finsler/ Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions w...

Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quaternionic projective spaces all of whose geodesics are (geometrical) circles.