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Mathematische Annalen, ISSN 0025-5831, 8/2016, Volume 365, Issue 3, pp. 1379 - 1408
In this paper a special class of Finsler metrics defined by a Riemannian metric and an 1-form is studied. The projectively flat metrics in dimension $$n\ge 3$$... 
Mathematics, general | Mathematics | 53B40 | 53C60
Journal Article
OSAKA JOURNAL OF MATHEMATICS, ISSN 0030-6126, 10/2015, Volume 52, Issue 4, pp. 1143 - 1162
From radial curvature geometry's standpoint, we prove a few sphere theorems of the Grove-Shiohama type for certain classes of compact Finsler manifolds. 
MATHEMATICS | CURVATURE | 53C60 | 53C22 | 53C21
Journal Article
Arabian Journal of Mathematics, ISSN 2193-5343, 6/2019, Volume 8, Issue 2, pp. 153 - 160
The class of stretch metrics contains the class of Landsberg metrics and the class of R-quadratic metrics. In this paper, we show that a regular non-Randers... 
Mathematics, general | Mathematics | 53C25 | 53C60 | Curvature
Journal Article
Osaka Journal of Mathematics, ISSN 0030-6126, 2015, Volume 52, Issue 1, pp. 215 - 235
We study Hilbert geometries admitting similar singularities on their boundary to those of a simplex. We show that in an adapted neighborhood of those... 
MATHEMATICS | HYPERBOLICITY | VOLUME | 53C24 | 51F99 | 53C60
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2013, Volume 357, Issue 2, pp. 711 - 726
We prove that if a metric measure space satisfies the volume doubling condition and the Caffarelli–Kohn–Nirenberg inequality with the same exponent $$n \ge 3$$... 
Mathematics, general | Mathematics | 58J60 | 53C60 | 35R06 | MATHEMATICS | MANIFOLDS | SYMMETRIZATION | SOBOLEV | Equality
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7129 - 7148
Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in... 
MATHEMATICS | CONVEX-BODIES | AFFINE SURFACE | STEPWISE APPROXIMATION
Journal Article
Journal of Geometry, ISSN 0047-2468, 12/2018, Volume 109, Issue 3, pp. 1 - 8
In this paper, we prove that a strongly convex complex Finsler metric F on a domain $$D\subset \mathbb {C}^n$$ D⊂Cn is projectively flat (resp. dually flat) if... 
Geometry | dually flat | 53C40 | Mathematics | 53C60 | projectively flat | Strongly convex complex Finsler metric
Journal Article
Advances in Geometry, ISSN 1615-715X, 07/2018, Volume 18, Issue 3, pp. 373 - 384
We investigate a class of complex Finsler metrics on a domain ⊂ ℂ . Necessary and sufficient conditions for these metrics to be strongly pseudoconvex complex... 
53C40 | Complex Finsler metric | 53C60 | complex Berwald metric | holomorphic curvature | MATHEMATICS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 02/2020, Volume 70, Issue 1, pp. 161 - 172
In this paper, we prove that every non-Riemannian 4-th root metric of isotropic scalar curvature has vanishing scalar curvature. Then, we show that every 4-th... 
4-th root metric | weakly isotropic flag curvature | Secondary 53C60 | scalar curvature | Primary 53B40 | MATHEMATICS | FLAT FINSLER METRICS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 03/2017, Volume 290, Issue 4, pp. 570 - 582
The contribution of this paper is two‐fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with... 
Finsler geometry | minimal surface | 53B40 | Randers space | hyperbolic space | Finsler metric | 53C60 | MATHEMATICS | BERNSTEIN TYPE THEOREMS
Journal Article
by Wu, B Y and Wu, B Y and Xin, Y L and Xin, Y L
Mathematische Annalen, ISSN 0025-5831, 1/2007, Volume 337, Issue 1, pp. 177 - 196
We prove Hessian comparison theorems, Laplacian comparison theorems and volume comparison theorems for Finsler manifolds under various curvature conditions. As... 
Mathematics, general | Mathematics | Secondary 53B40 | Primary 53C60 | MATHEMATICS | CURVATURE
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 8/2014, Volume 171, Issue 1, pp. 119 - 148
The present paper studies globally defined Kropina metrics as solutions of the Zermelo’s navigation problem. Moreover, we characterize the Kropina metrics of... 
Geometry | Killing vector fields | Riemannian isometries | 53C20 | Kropina spaces | Flag curvature | Mathematics | 53C60 | MATHEMATICS | SPACES | CONSTANT CURVATURE
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 6/2012, Volume 158, Issue 1, pp. 353 - 364
We investigate projective spherically symmetric Finsler metrics with constant flag curvature in R n and give the complete classification theorems. Furthermore,... 
Geometry | Spherical symmetry | 53B40 | 58B20 | Projective | Mathematics | 53C60 | Constant flag curvature | Bryant metric
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 3/2016, Volume 72, Issue 1, pp. 29 - 36
In 2000, Bejancu–Farran introduced the class of generalized Landsberg manifolds which contains the class of Landsberg manifolds. In this paper, we prove three... 
Mathematics, general | Mathematics | Landsberg manifold | 53C25 | 53C60 | Riemannian curvature | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | CONNECTIONS | FINSLER METRICS
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2011, Volume 351, Issue 2, pp. 365 - 392
In this paper we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular we present a fully detailed... 
Mathematics, general | 58E05 | Mathematics | 53C50 | 53C60 | 53C22 | MATHEMATICS | GENERAL-RELATIVITY | GEODESICS | THEOREM | SPACES | FERMAT PRINCIPLE
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 25
A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we study geodesic circles and (infinitesimal)... 
Einstein metric | 53B40 | Geodesic circle | lie derivative | Cartan Y -connection | Mathematics, general | Mathematics | 53C60 | conformal/concircular transformation | flag curvature | MATHEMATICS | MATHEMATICS, APPLIED | Cartan Y-connection | conformal | concircular transformation
Journal Article
Acta Universitatis Sapientiae, Mathematica, ISSN 1844-6094, 08/2018, Volume 10, Issue 1, pp. 167 - 177
The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in... 
Cartan space | 53B40 | exponential metric | Finsler space | 53C60 | duality between Finsler and Cartan spaces
Journal Article
Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 07/2017, Volume 25, Issue 2, pp. 85 - 99
The aim of this paper is to produce new examples of Riemannian and Finsler structures having as model a scalar deformation of conics inspired by the scaling... 
Secondary 51MB04 | Primary 53C60 | Finsler fundamental function | Finslerian flow | deformation | conic | invariant | Conic | Invariant | Deformation | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 12, pp. 2447 - 2464
Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in... 
34D23 | principal curvature | Funk metric | Mathematics | Applications of Mathematics | Finsler-Laplacian | isoparametric hypersurfaces | 53C60 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 1/2017, Volume 182, Issue 1, pp. 165 - 171
A connected Finsler space (M, F) is said to be homogeneous if it admits a transitive connected Lie group G of isometries. A geodesic in a homogeneous Finsler... 
53C30 | Homogeneous Finsler spaces | Geodesic vectors | Homogeneous geodesics | 53C22 | Mathematics, general | Mathematics | 53C60 | MATHEMATICS | MANIFOLDS
Journal Article
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