REVERSIBLE GEODESICS FOR (α, β)-METRICS

2010 ◽  
Vol 21 (08) ◽  
pp. 1071-1094 ◽  
Author(s):  
IOANA MONICA MASCA ◽  
VASILE SORIN SABAU ◽  
HIDEO SHIMADA
Keyword(s):  
Finsler Space ◽  
Finsler Metrics ◽  
Randers Space ◽  
Geodesic Paths

A Finsler space is said to have reversible geodesics if for any of its oriented geodesic paths, the same path traversed in the opposite sense is also a geodesic. In [6] the conditions for a Randers space to have reversible geodesics have been found. The main goal of this paper is to find conditions for a Finsler space endowed with an (α, β)-metric to be with reversible geodesics or strictly reversible geodesics, respectively. Moreover, we obtain some new classes of (α, β)-metrics with reversible geodesics and show how new Finsler metrics with reversible geodesics can be constructed by means of a Randers change.

Finsler Metrics with K = 0 and S = 0

2003 ◽  
Vol 55 (1) ◽  
pp. 112-132 ◽  
Author(s):  
Zhongmin Shen
Keyword(s):  
Euclidean Space ◽  
Shortest Path ◽  
External Force ◽  
Riemannian Space ◽  
Shortest Path Problem ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Randers Metric ◽  
Randers Space ◽  
Time Problem

AbstractIn the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.

WEAKLY SYMMETRIC FINSLER SPACES

2010 ◽  
Vol 12 (02) ◽  
pp. 309-323 ◽  
Author(s):  
SHAOQIANG DENG ◽  
ZIXIN HOU
Keyword(s):  
Open Problem ◽  
Finsler Space ◽  
Finsler Metrics ◽  
Dimensional Sphere ◽  
Finsler Spaces ◽  
Geometrical Properties ◽  
3 Dimensional ◽  
Weakly Symmetric

In this paper, we introduce the notion of weakly symmetric Finsler spaces and study some geometrical properties of such spaces. In particular, we prove that each maximal geodesic in a weakly symmetric Finsler space is the orbit of a one-parameter subgroup of the full isometric group. This implies that each weakly symmetric Finsler space has vanishing S-curvature. As an application of these results, we prove that there exist reversible non-Berwaldian Finsler metrics on the 3-dimensional sphere with vanishing S-curvature. This solves an open problem raised by Z. Shen.

scholarly journals On the ℒ-duality of a Finsler space with exponential metric αeβ/α

2018 ◽  
Vol 10 (1) ◽  
pp. 167-177
Author(s):  
Ramdayal Singh Kushwaha ◽  
Gauree Shanker
Keyword(s):  
Finsler Space ◽  
Finsler Geometry ◽  
Riemannian Metric ◽  
Finsler Metrics ◽  
Exponential Metric

Abstract 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 modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

scholarly journals KILLING FRAMES AND S-CURVATURE OF HOMOGENEOUS FINSLER SPACES

2014 ◽  
Vol 57 (2) ◽  
pp. 457-464 ◽  
Author(s):  
MING XU ◽  
SHAOQIANG DENG
Keyword(s):  
Explicit Formula ◽  
Vector Fields ◽  
Finsler Space ◽  
Killing Vector ◽  
Finsler Spaces ◽  
Killing Vector Fields ◽  
Randers Space ◽  
Homogeneous Finsler Space ◽  
Special Case

AbstractIn this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature. In the special case that the homogeneous Finsler space is a Randers space, we give an explicit formula which coincides with the previous formula obtained by the second author using other methods.

scholarly journals Deformation of complex Finsler metrics

2018 ◽  
Vol 26 (3) ◽  
pp. 229-244
Author(s):  
Annamária Szász-Friedl
Keyword(s):  
Finsler Space ◽  
Linear Connection ◽  
Finsler Metrics ◽  
Infinitesimal Deformation ◽  
Metric Tensor ◽  
First Order ◽  
Special Part ◽  
Non Linear ◽  
Order Deformation ◽  
Complex Finsler Metrics

AbstractThe aim of this paper is to describe the infinitesimal deformation (M, V) of a complex Finsler space family {(M, Lt)}t∈ℝ and to study some of its geometrical objects (metric tensor, non-linear connection, etc). In this circumstances the induced non-linear connection on (M, V) is defined. Moreover we have elaborate the inverse problem, the problem of the first order deformation of the metric. A special part is devoted to the study of particular cases of the perturbed metric.

Helicoidal Minimal Surfaces in a Finsler Space of Randers Type

2014 ◽  
Vol 57 (4) ◽  
pp. 765-779 ◽  
Author(s):  
Rosângela Maria da Silva ◽  
Keti Tenenblat
Keyword(s):  
Differential Equation ◽  
Minimal Surface ◽  
Minimal Surfaces ◽  
Finsler Space ◽  
Volume Form ◽  
Randers Metric ◽  
Euclidean Metric ◽  
Randers Space ◽  
Open Region ◽  
Fixed Axis

AbstractWe consider the Finsler space obtained by perturbing the Euclidean metric of ℝ3 by a rotation. It is the open region of ℝ3 bounded by a cylinder with a Randers metric. Using the Busemann–Hausdorff volume form, we obtain the differential equation that characterizes the helicoidal minimal surfaces in . We prove that the helicoid is a minimal surface in only if the axis of the helicoid is the axis of the cylinder. Moreover, we prove that, in the Randers space , the only minimal surfaces in the Bonnet family with fixed axis Ox̄3 are the catenoids and the helicoids.

scholarly journals Conformal Vector Fields on Finsler Space with Special (α , β )- Metric

2019 ◽  
pp. 1-8
Author(s):  
N. Natesh ◽  
S. K. Narasimhamurthy ◽  
M. K. Roopa
Keyword(s):  
Vector Fields ◽  
Finsler Space ◽  
Riemannian Metric ◽  
Finsler Metrics ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Beta 2

In this paper, we study the conformal vector elds on a class of Finsler metrics. In particular Finsler space with special (α, β)- metric `F =\alpha +\frac{\beta^2}{\alpha} ` is dened in Riemannian metric α and 1-form β and its norm. Then we characterize the PDE's of conformal vector elds on Finsler space with special (α, β)- metric.

On the theory of $4$-th root Finsler metrics

2019 ◽  
Vol 12 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Akbar Tayebi
Keyword(s):  
Finsler Metrics

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.

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