scholarly journals On the Class of (q,α,β)-Metrics

ISRN Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ahmad Alimohammadi
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Metric ◽  
Necessary And Sufficient Conditions ◽  
Finsler Metrics ◽  
Projectively Flat ◽  
Necessary And Sufficient

We study a class of Finsler metrics in the form F=α+βq/αq-1, where α is a Riemannian metric, β is a 1-form, and 1<q<2.  F is called (q,α,β)-metrics. We find the necessary and sufficient conditions under which the class of (q,α,β)-metrics is locally projectively flat and Douglas metrics, respectively.

scholarly journals Some Curvature Properties on Lorentzian Generalized Sasakian-Space-Forms

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Rongsheng Ma ◽  
Donghe Pei
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformally Flat ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Projectively Flat ◽  
Generalized Sasakian Space Form ◽  
Necessary And Sufficient

In this paper, we investigate the Lorentzian generalized Sasakian-space-form. We give the necessary and sufficient conditions for the Lorentzian generalized Sasakian-space-form to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric and their relationship between each other. As the application of our theorems, we study the Ricci almost soliton on conformally flat Lorentzian generalized Sasakian-space-form.

scholarly journals The projective curvature of the tangent bundle with natural diagonal metric

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 401-410 ◽  
Author(s):  
Cornelia-Livia Bejan ◽  
Simona-Luiza Druţă-Romaniuc
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Total Space ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Necessary And Sufficient

Our study is mainly devoted to a natural diagonal metric G on the total space TMof the tangent bundle of a Riemannian manifold (M, 1). We provide the necessary and sufficient conditions under which (TM,G) is a space form, or equivalently (TM,G) is projectively Euclidean. Moreover, we classify the natural diagonal metrics G for which (TM,G) is horizontally projectively flat (resp. vertically projectively flat).

On invariant Finsler metrics under (almost) β-changes

2017 ◽  
Vol 14 (11) ◽  
pp. 1750156
Author(s):  
Tahere Rajabi ◽  
Nasrin Sadeghzadeh ◽  
Maryam Maleki
Keyword(s):  
Special Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finsler Metrics ◽  
Necessary And Sufficient

In this paper, we are going to study some [Formula: see text]-changes of the special class of Finsler metrics which we refer to as the (almost) [Formula: see text]-change and generalized (almost) [Formula: see text]-conformal changes. We investigate Douglas and Weyl tensors under these changes. In particular, we find the necessary and sufficient conditions for the Douglas metrics to be invariant under these type of changes.

On projective invariants of spherically symmetric Finsler spaces in Rn

2015 ◽  
Vol 12 (07) ◽  
pp. 1550074 ◽  
Author(s):  
Nasrin Sadeghzadeh ◽  
Maedeh Hesamfar
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finsler Spaces ◽  
Projective Invariants ◽  
Necessary And Sufficient

In this paper, we study projective invariants of spherically symmetric Finsler metrics in Rn. We find the necessary and sufficient conditions for the metrics to be Weyl, Douglas and generalized Douglas–Weyl (GDW) types. In particular, we find the necessary and sufficient condition for the metrics to be of scalar flag curvature. Also we show that two classes of GDW and Douglas spherically symmetric Finsler metrics coincide.

On Projectively Flat (α, β)-metrics

2009 ◽  
Vol 52 (1) ◽  
pp. 132-144 ◽  
Author(s):  
Zhongmin Shen
Keyword(s):  
Riemannian Metric ◽  
Finsler Metrics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Regular Case ◽  
Projectively Flat ◽  
Necessary And Sufficient

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.

On conformally related spherically symmetric Finsler metrics

2016 ◽  
Vol 13 (10) ◽  
pp. 1650118 ◽  
Author(s):  
Maryam Maleki ◽  
Nasrin Sadeghzadeh ◽  
Tahereh Rajabi
Keyword(s):  
Einstein Metrics ◽  
Finsler Geometry ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Conformal Transformations ◽  
Conformal Change ◽  
Projective Invariant ◽  
Necessary And Sufficient

In this paper, we study the projective invariant quantities in Finsler geometry which remain invariant under the conformal change of metrics. In particular, we obtain the necessary and sufficient conditions of a given Douglas and Weyl and generalized Douglas–Weyl (GDW) metric to be invariant under the conformal transformations. Finally, we introduce some explicit examples of these metrics. Also, some of these [Formula: see text]-conformal transformations of Einstein metrics are considered.

On complex Berwald metrics which are not conformal changes of complex Minkowski metrics

2018 ◽  
Vol 18 (3) ◽  
pp. 373-384 ◽  
Author(s):  
Hongchuan Xia ◽  
Chunping Zhong
Keyword(s):  
Sufficient Conditions ◽  
Finsler Metrics ◽  
Hermitian Metrics ◽  
Strongly Convex ◽  
Projectively Flat ◽  
Convex Case ◽  
Minkowski Metrics ◽  
Complex Finsler Metrics ◽  
Necessary And Sufficient

AbstractWe investigate a class of complex Finsler metrics on a domain D ⊂ ℂn. Necessary and sufficient conditions for these metrics to be strongly pseudoconvex complex Finsler metrics, or complex Berwald metrics, are given. The complex Berwald metrics constructed in this paper are neither trivial Hermitian metrics nor conformal changes of complex Minkowski metrics. We give a characterization of complex Berwald metrics which are of isotropic holomorphic curvatures, and also give characterizations of complex Finsler metrics of this class to be Kähler Finsler or weakly Kähler Finsler metrics. Moreover, in the strongly convex case, we give characterizations of complex Finsler metrics of this class to be projectively flat Finsler metrics or dually flat Finsler metrics.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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