The Flag Curvature Tensor on a Closed Finsler Space

1999 ◽  
Vol 36 (1-2) ◽  
pp. 149-159 ◽  
Author(s):  
Xiaohuan Mo
Keyword(s):  
Curvature Tensor ◽  
Finsler Space ◽  
Flag Curvature

scholarly journals New classes of projectively related Finsler metrics of constant flag curvature

2020 ◽  
Vol 17 (05) ◽  
pp. 2050068
Author(s):  
Georgeta Creţu
Keyword(s):  
Curvature Tensor ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Text Type ◽  
Constant Flag Curvature ◽  
Projective Invariant

We define a Weyl-type curvature tensor of [Formula: see text]-type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel functions. Based on this aspect, we construct new families of projectively related Finsler metrics that have constant flag curvature.

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.

scholarly journals Decomposability of Projective Curvature Tensor in Recurrent Finsler Space (WR-F_n)

2014 ◽  
Vol 100 (19) ◽  
pp. 32-34
Author(s):  
Meenakshy Thakur ◽  
C. K. Mishra ◽  
Gautam Lodhi
Keyword(s):  
Curvature Tensor ◽  
Finsler Space ◽  
Projective Curvature ◽  
Projective Curvature Tensor

scholarly journals A special form of Rund's h-curvature tensor using $R3$-like Finsler space

2009 ◽  
Vol 3 ◽  
pp. 175-180
Author(s):  
S. T. Aveesh ◽  
S. K. Narasimhamurthy ◽  
H. G. Nagaraja ◽  
Pradeep Kumar
Keyword(s):  
Curvature Tensor ◽  
Special Form ◽  
Finsler Space

scholarly journals On complete Finsler spaces of constant negative Ricci curvature

2020 ◽  
Vol 17 (03) ◽  
pp. 2050041
Author(s):  
Behroz Bidabad ◽  
Maryam Sepasi
Keyword(s):  
Ricci Curvature ◽  
Schwarzian Derivative ◽  
Finsler Space ◽  
Ricci Scalar ◽  
Flag Curvature ◽  
Finsler Spaces ◽  
Randers Metric

Here, using the projectively invariant pseudo-distance and Schwarzian derivative, it is shown that every connected complete Finsler space of the constant negative Ricci scalar is reversible. In particular, every complete Randers metric of constant negative Ricci (or flag) curvature is Riemannian.

Cosmological Consequences with Randers Conformal of Finsler space

2007 ◽  
Vol 3 (2) ◽  
pp. 203-211
Author(s):  
Arunesh Pandey ◽  
R K Mishra
Keyword(s):  
Background Radiation ◽  
Finsler Space ◽  
Space Time ◽  
Anisotropic Model ◽  
Microwave Background ◽  
Microwave Background Radiation

In this paper we study an anisotropic model of space – time with Finslerian metric. The observed anisotropy of the microwave background radiation is incorporated in the Finslerian metric of space time.

THE STUDY OF BERWALD CONNECTION OF A FINSLER SPACE WITH A SPECIAL (α,β)-METRIC

2020 ◽  
Vol 9 (6) ◽  
pp. 3221-3228
Author(s):  
V. D. Mylarappa ◽  
N. S. Kampalappa
Keyword(s):  
Finsler Space ◽  
Berwald Connection

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

Generalized Riemann spaces

1956 ◽  
Vol 52 (4) ◽  
pp. 623-625 ◽  
Author(s):  
John Moffat
Keyword(s):  
Curvature Tensor ◽  
Physical Theory ◽  
Dimensional Space ◽  
Riemann Space ◽  
Recent Attempt ◽  
Fundamental Tensor ◽  
Fundamental Properties ◽  
Complex Symmetric ◽  
Definition Of ◽  
Generalized Curvature Tensor

ABSTRACTThe recent attempt at a physical interpretation of non-Riemannian spaces by Einstein (1, 2) has stimulated a study of these spaces (3–8). The usual definition of a non-Riemannian space is one of n dimensions with which is associated an asymmetric fundamental tensor, an asymmetric linear affine connexion and a generalized curvature tensor. We can also consider an n-dimensional space with which is associated a complex symmetric fundamental tensor, a complex symmetric affine connexion and a generalized curvature tensor based on these. Some aspects of this space can be compared with those of a Riemann space endowed with two metrics (9). In the following the fundamental properties of this non-Riemannian manifold will be developed, so that the relation between the geometry and physical theory may be studied.

Sign in / Sign up

Export Citation Format

Share Document