Open AccessJournal Article
On Finsler spaces of Douglas type. A generalization of the notion of Berwald space
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This article is published in Publicationes Mathematicae Debrecen.The article was published on 1997-01-01 and is currently open access. It has received 160 citations till now. The article focuses on the topics: Space (mathematics) & Generalization.read more
Citations
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Journal ArticleDOI
Zermelo navigation on Riemannian manifolds
TL;DR: In this paper, the authors studied Zermelo navigation on Riemannian manifolds and used that to solve a long standing problem in Finsler geometry, namely the complete classification of strongly convex Randers metrics of constant flag curvature.
Book
The Geometry of Hamilton and Lagrange Spaces
TL;DR: The duality between Lagrange and Hamilton spaces is discussed in this paper, where the dual bundle of a k-osculator bundle is defined as Cartan spaces of order 2.
Posted Content
Finsler Metrics with K=0 and S=0
TL;DR: In this paper, the authors introduce a technique to construct non-projectively flat Finsler metrics with zero curvature in each dimension, which can be used to construct many nonprojective flat FING metrics of constant curvature.
MonographDOI
Differential Geometry of Special Mappings
Josef Mikeš,Elena Stepanova,Alena Vanžurová,Bácso Sándor,Vladimir Berezovski,Elena Chepurna,Marie Chodorová,Hana Chudá,Michail Gavrilchenko,Michael Haddad,Irena Hinterleitner,Marek Jukl,Lenka Juklová,Dzhanybek Moldobaev,Patrik Peška,I. G. Shandra,Mohsen Shiha,Dana Smetanová,Sergej Stepanov,Vasilij Sobchuk,Irina Tsyganok +20 more
TL;DR: The theory of manifolds with affine connection has been studied in this paper, where the authors deal with the theory of conformal, geodesic, and projective mappings and transformations.
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On the Flag Curvature of Finsler Metrics of Scalar Curvature
TL;DR: In this paper, the flag curvature of a Finsler metric is defined as a scalar function on the slit tangent bundle, and the curvature is determined when certain non-Riemannian quantities such as Cartan torsion and Landsberg curvature are isotropic.
References
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On Finsler and Cartan Geometries. III: Two-Dimensional Finsler Spaces with Rectilinear Extremals
TL;DR: In this article, the main scalar of a two-dimensional Finsler space with rectilinear extremals is characterized in an invariant manner, in a suitable coordinate system, by linear equations.
Journal ArticleDOI
Two-dimensional Finsler spaces whose geodesics constitute a family of special conic sections
Theory of extended point transformations of Finsler spaces. II : Fundamental theorems of projective motions
TL;DR: In this paper, the transformations ponctuelles etendues des espaces de Finsler are studied, and theoremes fondamentaux de mouvements projectifs are discussed.