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 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.

Gap theorems for compact almost Ricci-harmonic solitons

2019 ◽  
Vol 30 (08) ◽  
pp. 1950040 ◽  
Author(s):  
Abimbola Abolarinwa
Keyword(s):  
Einstein Metrics ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Compact Domain ◽  
Necessary And Sufficient ◽  
Gap Theorems

Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. The main focus of this paper is to establish necessary and sufficient conditions for a gradient shrinking almost Ricci-harmonic soliton on a compact domain to be almost harmonic-Einstein.

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.

Projective Ricci flat spherically symmetric Finsler metrics

2018 ◽  
Vol 29 (11) ◽  
pp. 1850078 ◽  
Author(s):  
Hongmei Zhu ◽  
Haixia Zhang
Keyword(s):  
Ricci Curvature ◽  
Finsler Geometry ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Projective Invariant ◽  
Ricci Flat ◽  
Douglas Metric

In Finsler geometry, the projective Ricci curvature is an important projective invariant. In this paper, we characterize projective Ricci flat spherically symmetric Finsler metrics. Under a certain condition, we prove that a projective Ricci flat spherically symmetric Finsler metric must be a Douglas metric. Moreover, we construct a class of new nontrivial examples on projective Ricci flat Finsler metrics.

On generalized 4-th root metrics of isotropic scalar curvature

2018 ◽  
Vol 68 (4) ◽  
pp. 907-928 ◽  
Author(s):  
Akbar Tayebi
Keyword(s):  
Scalar Curvature ◽  
Finsler Geometry ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Sufficient Condition ◽  
Riemannian Curvature ◽  
Necessary And Sufficient Condition ◽  
Conformal Change ◽  
Riemannian Curvature Tensor ◽  
Necessary And Sufficient

AbstractBy an interesting physical perspective and a suitable contraction of the Riemannian curvature tensor in Finsler geometry, Akbar-Zadeh introduced the notion of scalar curvature for the Finsler metrics. A Finsler metric is called of isotropic scalar curvature if the scalar curvature depends on the position only. In this paper, we study the class of generalized 4-th root metrics. These metrics generalize 4-th root metrics which are used in Biology as ecological metrics. We find the necessary and sufficient condition under which a generalized 4-th root metric is of isotropic scalar curvature. Then, we find the necessary and sufficient condition under which the conformal change of a generalized 4-th root metric is of isotropic scalar curvature. Finally, we characterize the Bryant metrics of isotropic scalar curvature.

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.

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.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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