SOME RESULTS ON THE NON-RIEMANNIAN QUANTITY H OF A FINSLER METRIC

2011 ◽  
Vol 22 (07) ◽  
pp. 925-936 ◽  
Author(s):  
QIAOLING XIA
Keyword(s):  
Finsler Geometry ◽  
Finsler Manifold ◽  
Finsler Metric ◽  
Randers Metric ◽  
Rigidity Theorems

In this paper, we study the non-Riemannian quantity H in Finsler geometry. We obtain some rigidity theorems of a compact Finsler manifold under some conditions related to H. We also prove that the S-curvature for a Randers metric is almost isotropic if and only if H almost vanishes. In particular, S-curvature is isotropic if and only if H = 0.

scholarly journals A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY

2012 ◽  
Vol 54 (3) ◽  
pp. 637-645 ◽  
Author(s):  
XIAOHUAN MO ◽  
ZHONGMIN SHEN ◽  
HUAIFU LIU
Keyword(s):  
Scalar Curvature ◽  
Simple Proof ◽  
Finsler Geometry ◽  
Finsler Manifold ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Riemannian Curvature

AbstractIn this note, we study a new Finslerian quantity Ĉ defined by the Riemannian curvature. We prove that the new Finslerian quantity is a non-Riemannian quantity for a Finsler manifold with dimension n = 3. Then we study Finsler metrics of scalar curvature. We find that the Ĉ-curvature is closely related to the flag curvature and the H-curvature. We show that Ĉ-curvature gives, a measure of the failure of a Finsler metric to be of weakly isotropic flag curvature. We also give a simple proof of the Najafi-Shen-Tayebi' theorem.

scholarly journals The Β-Change by Finsler Metric of C-Reducible Finsler Spaces in Finsler Geometry

2019 ◽  
Vol 33 (1) ◽  
pp. 1-10
Author(s):  
Khageswar Mandal
Keyword(s):  
Finsler Space ◽  
Homogeneous Function ◽  
Finsler Geometry ◽  
Finsler Metric ◽  
Finsler Spaces

 This paper considered about the β-Change of Finsler metric L given by L*= f(L, β), where f is any positively homogeneous function of degree one in L and β and obtained the β-Change by Finsler metric of C-reducible Finsler spaces. Also further obtained the condition that a C-reducible Finsler space is transformed to a C-reducible Finsler space by a β-change of Finsler metric.

scholarly journals METRIC COMPATIBLE OR NON-COMPATIBLE FINSLER–RICCI FLOWS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250041 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Ricci Flow ◽  
Evolution Equations ◽  
Finsler Geometry ◽  
Flow Theory ◽  
Finsler Metric ◽  
Geometric Evolution ◽  
Ricci Flows ◽  
Canonical Metric ◽  
Self Consistent ◽  
Math Phys

There were elaborated different models of Finsler geometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible) connections, the Ricci flag curvature, etc. In a series of works, we studied (non)-commutative metric compatible Finsler and non-holonomic generalizations of the Ricci flow theory [see S. Vacaru, J. Math. Phys. 49 (2008) 043504; 50 (2009) 073503 and references therein]. The aim of this work is to prove that there are some models of Finsler gravity and geometric evolution theories with generalized Perelman's functionals, and correspondingly derived non-holonomic Hamilton evolution equations, when metric non-compatible Finsler connections are involved. Following such an approach, we have to consider distortion tensors, uniquely defined by the Finsler metric, from the Cartan and/or the canonical metric compatible connections. We conclude that, in general, it is not possible to elaborate self-consistent models of geometric evolution with arbitrary Finsler metric non-compatible connections.

ON SPHERICALLY SYMMETRIC FINSLER METRICS WITH ISOTROPIC BERWALD CURVATURE

2013 ◽  
Vol 10 (10) ◽  
pp. 1350054 ◽  
Author(s):  
ENLI GUO ◽  
HUAIFU LIU ◽  
XIAOHUAN MO
Keyword(s):  
Orthogonal Group ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Randers Metric

A Finsler metric F is said to be spherically symmetric if the orthogonal group O(n) acts as isometries of F. In this paper, we show that every spherically symmetric Finsler metric of isotropic Berwald curvature is a Randers metric. We also construct explicitly a lot of new isotropic Berwald spherically symmetric Finsler metrics.

scholarly journals The Existence of Two Homogeneous Geodesics in Finsler Geometry

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 850
Author(s):  
Zdeněk Dušek
Keyword(s):  
Finsler Geometry ◽  
Finsler Manifold ◽  
Finsler Manifolds ◽  
Homogeneous Geodesics ◽  
Homogeneous Geodesic ◽  
Randers Metrics

The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible.

Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ming Xu
Keyword(s):  
Lie Algebra ◽  
Finsler Space ◽  
Finsler Manifold ◽  
Constant Speed ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Coset Space ◽  
Finsler Spaces ◽  
Negatively Curved ◽  
Positively Curved

Abstract We study the interaction between the g.o. property and certain flag curvature conditions. A Finsler manifold is called g.o. if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also consider the condition (FP) for the flag curvature, i.e. in any flag we find a flag pole such that the flag curvature is positive. By our main theorem, if a g.o. Finsler space (M, F) has non-negative flag curvature and satisfies (FP), then M is compact. If M = G/H where G has a compact Lie algebra, then the rank inequality rk 𝔤 ≤ rk 𝔥+1 holds. As an application,we prove that any even-dimensional g.o. Finsler space which has non-negative flag curvature and satisfies (FP) is a smooth coset space admitting a positively curved homogeneous Riemannian or Finsler metric.

ON COMPLEX RANDERS METRICS

2010 ◽  
Vol 21 (08) ◽  
pp. 971-986 ◽  
Author(s):  
BIN CHEN ◽  
YIBING SHEN
Keyword(s):  
Finsler Geometry ◽  
Randers Metric ◽  
Holomorphic Curvature ◽  
Randers Metrics

A characteristic for a complex Randers metric to be a complex Berwald metric is obtained. The formula of the holomorphic curvature for complex Randers metrics is given. It is shown that a complex Berwald Randers metric with isotropic holomorphic curvature must be either usually Kählerian or locally Minkowskian. The Deicke and Brickell theorems in complex Finsler geometry are also proved.

TOTALLY GEODESIC SUBMANIFOLDS OF GL-MANIFOLDS

2012 ◽  
Vol 09 (01) ◽  
pp. 1250002
Author(s):  
ABOLGHASEM LALEH ◽  
MORTEZA M. REZAII ◽  
ATAABAK BAAGHERZADEH HUSHMANDI
Keyword(s):  
Riemannian Manifold ◽  
Finsler Manifold ◽  
Finsler Metric ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Totally Geodesic ◽  
Geodesic Submanifolds ◽  
Totally Geodesic Submanifolds ◽  
Necessary And Sufficient ◽  
Sasakian Metric

In this paper, for a Finsler manifold (M, F) with a Finsler metric gij(x, y) we shall consider a generalized Lagrange metrics (FGL-metrics) as the form *gij(x, y) = gij(x, y) + σ(x, y)Bi(x, y)Bj(x, y) on TM. Then we shall consider a Riemannian manifold (TM, *G) in which *G is a generalized Sasakian metric of *g on [Formula: see text]. Then we restrict the above FGL-metrics to a submanifold of [Formula: see text], and show that it admits a GL-metric structure. Then we shall find a necessary and sufficient condition for this submanifold to be totally geodesic.

Sign in / Sign up

Export Citation Format

Share Document