Some formulas of Gauss-Bonnet-Chern type in Riemann-Finsler geometry.
Some generalized comparison results in Finsler geometry and their applications
In this paper, we generalize the Hessian comparison theorems and Laplacian comparison theorems described in [16, 18], then give some applications under various curvature conditions.
Some results on the geometry of Minkowski plane
In this paper we study the geometry of Minkowski plane and obtain some results. We focus on the curve theory in Minkowski plane and prove that the total curvature of any simple closed curve equals to the total Landsberg angle. As the result, the sum of oriented exterior Landsberg angles of any polygon is also equal to the total Landsberg angle, and when the Minkowski plane is reversible, the sum of interior Landsberg angles of any -gon is times of the total Landsberg angle. Our results generalizes...
Some rigidity theorems for Finsler manifolds.
Some rigidity theorems for Finsler manifolds of sectional flag curvature
In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.
Spherically symmetric generalized Lagrange metrics.
Stable harmonic maps between Finsler manifolds and Riemannian manifolds with positive Ricci curvature
We study the stability of harmonic maps between Finsler manifolds and Riemannian manifolds with positive Ricci curvature, and we prove that if Mⁿ is a compact Einstein Riemannian minimal submanifold of a Riemannian unit sphere with Ricci curvature satisfying , then there is no non-degenerate stable harmonic map between M and any compact Finsler manifold.
Structure of geodesics in weakly symmetric Finsler metrics on H-type groups
Structure of geodesic graphs in special families of invariant weakly symmetric Finsler metrics on modified H-type groups is investigated. Geodesic graphs on modified H-type groups with the center of dimension or are constructed. The new patterns of algebraic complexity of geodesic graphs are observed.
Submanifolds and the Hofer norm
In [Ch00], Chekanov showed that the Hofer norm on the Hamiltonian diffeomorphism group of a geometrically bounded symplectic manifold induces a nondegenerate metric on the orbit of any compact Lagrangian submanifold under the group. In this paper we consider the orbits of more general submanifolds. We show that, for the Chekanov–Hofer pseudometric on the orbit of a closed submanifold to be a genuine metric, it is necessary for the submanifold to be coisotropic, and we show that this condition is...
Sur la géométrie du fibré tangent à une variété finslérienne compactes
Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope
En utilisant la version de Spencer-Goldschmidt du théorème de Cartan-Kähler nous étudions les conditions nécessaires et suffisantes pour qu’un système d’équations différentielles ordinaires du second ordre soit le système d’Euler-Lagrange associé à un lagrangien régulier. Dans la thèse de Z. Muzsnay cette technique a été déjà appliquée pour donner une version moderne du papier classique de Douglas qui traite le cas de la dimension 2. Ici nous considérons le cas où la dimension est arbitraire, nous...
Sur l’entropie volumique des géométries de Hilbert
Nous présentons ici une étude complémentaire de notre travail en collaboration avec G. Berck et A. Bernig sur l’entropie volumique des géométries de Hilbert. Outre la présentation de nos résultats dont les démonstrations sont accessibles dans le travail susmentionné, on trouvera ici des exemples de géométrie pour lesquels le calcul de l’entropie est possible ainsi que diverses remarques quant aux conséquences de nos travaux.
The affine approach to homogeneous geodesics in homogeneous Finsler spaces
In the recent paper [Yan, Z.: Existence of homogeneous geodesics on homogeneous Finsler spaces of odd dimension, Monatsh. Math. 182,1, 165–171 (2017)], it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. However, the proof contains a serious gap. The situation is a bit delicate, because the statement is correct. In the present paper, the incorrect part in this proof is indicated. Further, it is shown that homogeneous geodesics in homogeneous...
The concept of invariant geometry of second order.
The Critical Points Theory for the Closed Geodesics Problem.
The curvature theory of generalized connection in .
The explicit construction of Einstein Finsler metrics with non-constant flag curvature.
The geometry of autonomous metrical multi-time Lagrange space of electrodynamics.
The homogeneous lift on the cotangent bundle.
The Induced Connections on the Subspaces in Miron's Osckm