scholarly journals Weighted projective Ricci curvature in Finsler geometry

2021 ◽  
Vol 71 (1) ◽  
pp. 183-198
Author(s):  
Tayebeh Tabatabaeifar ◽  
Behzad Najafi ◽  
Akbar Tayebi
Keyword(s):  
Ricci Curvature ◽  
Finsler Geometry ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Randers Metric ◽  
Ricci Flat ◽  
Projectively Flat ◽  
Flat Metric ◽  
Necessary And Sufficient ◽  
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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
D. G. Prakasha ◽  
Shyamal Kumar Hui ◽  
Kakasab Mirji
Keyword(s):  
Constant Curvature ◽  
Space Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Forms ◽  
3 Dimensional ◽  
Projectively Flat ◽  
Necessary And Sufficient

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.

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 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.

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

2017 ◽  
Vol 18 ◽  
pp. 1-12
Author(s):  
Maranna Ramesha ◽  
S.K. Narasimhamurthy
Keyword(s):  
Present Article ◽  
Finsler Space ◽  
Riemannian Metric ◽  
Sufficient Condition ◽  
Important Class ◽  
Necessary And Sufficient Condition ◽  
Berwald Space ◽  
Projectively Flat ◽  
Necessary And Sufficient

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 generalized Kropina change of mth root Finsler metric

2017 ◽  
Vol 14 (05) ◽  
pp. 1750081 ◽  
Author(s):  
Bankteshwar Tiwari ◽  
Ghanashyam Kr. Prajapati
Keyword(s):  
Finsler Metric ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Projectively Flat ◽  
Necessary And Sufficient

In the present paper, we consider generalized Kropina change of [Formula: see text]th root Finsler metric and prove that it is locally projectively flat if and only if it is locally Minkowskian. We also establish a necessary and sufficient condition under which the generalized Kropina change of [Formula: see text]th root metric is locally dually flat. Further it is proved that a generalized Kropina change of [Formula: see text]th root metric cannot be conformal to an [Formula: see text]th root Finsler metric.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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