Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric

Berwald Space ◽

Projectively Flat ◽

The present article is organized as follows: In the first part, we characterize the important class of special Finsler (α,β)-metric in the form ofL=α+α2/β, whereαis Riemannian metric andβis differential 1-form to be projectively flat. In the second part, we describe condition for a Finsler spaceFnwith an (α,β)-metric is of Douglas type. Further we investigate the necessary and sufficient condition for a Finsler space with an (α,β)-metric to be weakly-Berwald space and Berwald space.

On Projectively Flat (α, β)-metrics

Canadian Mathematical Bulletin ◽

10.4153/cmb-2009-016-2 ◽

2009 ◽

Vol 52 (1) ◽

pp. 132-144 ◽

Cited By ~ 31

Author(s):

Zhongmin Shen

Keyword(s):

Riemannian Metric ◽

Finsler Metrics ◽

Sufficient Condition ◽

Regular Case ◽

Projectively Flat ◽

AbstractThe solutions to Hilbert's Fourth Problem in the regular case are projectively flat Finsler metrics. In this paper, we consider the so-called (α, β)-metrics defined by a Riemannian metric α and a 1-form β, and find a necessary and sufficient condition for such metrics to be projectively flat in dimension n ≥ 3.

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

Subexponential distribution functions

10.1017/s1446788700021340 ◽

1980 ◽

Vol 29 (3) ◽

pp. 337-347 ◽

Cited By ~ 90

Author(s):

E. J. G. Pitman

Keyword(s):

Distribution Function ◽

Comparison Theorem ◽

Distribution Functions ◽

Sufficient Condition ◽

Important Class ◽

Closure Properties ◽

Subexponential Class ◽

60 J 80

AbstractA distribution function (F on [0,∞) belongs to the subexponential class if and only if 1−F(2) (x) ~ 2(1−F(x)), as x→ ∞. For an important class of distribution functions, a simple, necessary and sufficient condition for membership of is given. A comparison theorem for membership of and also some closure properties of are obtained.1980 Mathematics subject classification (Amer. Math. Soe.): primary 60 E 05; secondary 60 J 80.

Killing Vector Fields in Generalized Conformalβ-Change of Finsler Spaces

Journal of Mathematics ◽

10.1155/2015/456291 ◽

2015 ◽

Vol 2015 ◽

pp. 1-5

Author(s):

Mallikarjun Yallappa Kumbar ◽

Narasimhamurthy Senajji Kampalappa ◽

Thippeswamy Komalobiah Rajanna ◽

Kavyashree Ambale Rajegowda

Keyword(s):

Vector Field ◽

Vector Fields ◽

Finsler Space ◽

Killing Vector ◽

Sufficient Condition ◽

Finsler Spaces ◽

Killing Vector Fields ◽

We consider a Finsler space equipped with a Generalized Conformalβ-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformalβ-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformalβ-change of metric.

On An Affine Connection Which Admits A Volume-Like Form

Canadian Mathematical Bulletin ◽

10.4153/cmb-1990-077-6 ◽

1990 ◽

Vol 33 (4) ◽

pp. 482-488 ◽

Cited By ~ 1

Author(s):

D. P. Chi ◽

Y. D. Yoon

Keyword(s):

Affine Connection ◽

Riemannian Metric ◽

Necessary Condition ◽

Sufficient Condition ◽

Riemannian Connection ◽

Cech Cohomology ◽

AbstractA necessary and sufficient condition to obtain a volumelike form from an affine connection is given in terms of the Čech cohomology, after the volume-like form is naturally defined without a Riemannian metric. A necessary condition for an affine connection to be a Riemannian connection for some metric is also given.

On the notion ofL 1-completeness of a stochastic flow on a manifold

Abstract and Applied Analysis ◽

10.1155/s1085337502206053 ◽

2002 ◽

Vol 7 (12) ◽

pp. 627-635 ◽

Cited By ~ 1

Author(s):

Yu. E. Gliklikh ◽

L. A. Morozova

Keyword(s):

Functional Space ◽

Riemannian Metric ◽

Stochastic Flow ◽

Time Interval ◽

Sufficient Condition ◽

The Given

We introduce the notion ofL 1-completeness for a stochastic flow on manifold and prove a necessary and sufficient condition for a flow to beL 1-complete.L 1-completeness means that the flow is complete (i.e., exists on the given time interval) and that it belongs to some sort ofL 1-functional space, natural for manifolds where no Riemannian metric is specified.

NATURAL CONNECTION WITH TOTALLY SKEW-SYMMETRIC TORSION ON RIEMANNIAN ALMOST PRODUCT MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781250003x ◽

2012 ◽

Vol 09 (01) ◽

pp. 1250003 ◽

Cited By ~ 2

Author(s):

DIMITAR MEKEROV ◽

MANCHO MANEV

Keyword(s):

Linear Connection ◽

Riemannian Metric ◽

Sufficient Condition ◽

Product Manifold ◽

Natural Connection ◽

Almost Product Manifold ◽

Hermitian Geometry ◽

Levi Civita Connection ◽

On a Riemannian almost product manifold (M, P, g), we consider a linear connection preserving the almost product structure P and the Riemannian metric g and having a totally skew-symmetric torsion. We determine the class of the manifolds (M, P, g) admitting such a connection and prove that this connection is unique in terms of the covariant derivative of P with respect to the Levi-Civita connection. We find a necessary and sufficient condition the curvature tensor of the considered connection to have similar properties like the ones of the Kähler tensor in Hermitian geometry. We pay attention to the case when the torsion of the connection is parallel. We consider this connection on a Riemannian almost product manifold (G, P, g) constructed by a Lie group G.

Weighted projective Ricci curvature in Finsler geometry

Mathematica Slovaca ◽

10.1515/ms-2017-0446 ◽

2021 ◽

Vol 71 (1) ◽

pp. 183-198

Author(s):

Tayebeh Tabatabaeifar ◽

Behzad Najafi ◽

Akbar Tayebi

Keyword(s):

Ricci Curvature ◽

Finsler Geometry ◽

Sufficient Condition ◽

Randers Metric ◽

Ricci Flat ◽

Projectively Flat ◽

Flat Metric ◽

Randers Metrics

Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

On 3-Dimensional Contact Metric Generalized(k,μ)-Space Forms

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2014/797162 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

D. G. Prakasha ◽

Shyamal Kumar Hui ◽

Kakasab Mirji

Keyword(s):

Constant Curvature ◽

Space Form ◽

Sufficient Condition ◽

Space Forms ◽

3 Dimensional ◽

Projectively Flat ◽

The present paper deals with a study of 3-dimensional contact metric generalized(k,μ)-space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized(k,μ)-space form withQϕ=ϕQto be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric andξ-projectively flat, respectively.

h-EXPONENTIAL CHANGE OF FINSLER METRIC

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1605029g ◽

2017 ◽

pp. 1029

Author(s):

Manish Kumar Gupta ◽

Anil K. Gupta

Keyword(s):

Finsler Space ◽

Finsler Metric ◽

Sufficient Condition ◽

Cartan Connection ◽

Connection Coefficients ◽

Exponential Change

In this paper, we studied a Finsler space whose metric is given by an h-exponential change and obtain the Cartan connection coefficients for the change. We also find the necessary and sufficient condition for an h-exponential change of Finsler metric to be projective.

Four-Dimensional Semi-Riemannian Szabó Manifolds

Journal of Mathematics ◽

10.1155/2020/6663361 ◽

2020 ◽

Vol 2020 ◽

pp. 1-5

Author(s):

Abdoul Salam Diallo ◽

Punam Gupta

Keyword(s):

Ricci Tensor ◽

Riemannian Metric ◽

Sufficient Condition ◽

Affine Surface ◽

In this paper, we prove that the deformed Riemannian extension of any affine Szabó manifold is a Szabó pseudo-Riemannian metric and vice versa. We prove that the Ricci tensor of an affine surface is skew-symmetric and nonzero everywhere if and only if the affine surface is Szabó. We also find the necessary and sufficient condition for the affine Szabó surface to be recurrent. We prove that, for an affine Szabó recurrent surface, the recurrence covector of a recurrence tensor is not locally a gradient.