scholarly journals On the classification of Landsberg spherically symmetric Finsler metrics

2021 ◽  
Author(s):  
S. G. Elgendi
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Higher Dimensions ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Two Dimensional ◽  
Compatibility Conditions ◽  
Symmetric Metrics ◽  
Specific Formula

In this paper, as an application of the inverse problem of calculus of variations, we investigate two compatibility conditions on the spherically symmetric Finsler metrics. By making use of these conditions, we focus our attention on the Landsberg spherically symmetric Finsler metrics. We classify all spherically symmetric manifolds of Landsberg or Berwald types. For the higher dimensions [Formula: see text], we prove that all Landsberg spherically symmetric manifolds are either Riemannian or their geodesic sprays have a specific formula; all regular Landsberg spherically symmetric metrics are Riemannian; all (regular or non-regular) Berwald spherically symmetric metrics are Riemannian. Moreover, we establish new unicorns, i.e. new explicit examples of non-regular non-Berwaldian Landsberg metrics are obtained. For the two-dimensional case, we characterize all Berwald or Landsberg spherically symmetric surfaces.

An Inverse Problem in the Calculus of Variations and the Characteristic Curves of Connections on SO(3)-Bundles

1995 ◽  
Vol 38 (2) ◽  
pp. 129-140 ◽  
Author(s):  
Richard Atkins ◽  
Zhong Ge
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Ricci Tensor ◽  
Riemannian Metric ◽  
Two Dimensional ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Characteristic Curves ◽  
Riemannian Connection ◽  
Symmetric Connection

AbstractThis paper concerns an inverse problem in the calculus of variations, namely, when a two-dimensional symmetric connection is globally a Riemannian or pseudo-Riemannian connection. Two new local characterizations of such connections in terms of the Ricci tensor and the Riemann curvature tensor respectively are given, together with a solution to the global problem. As an application, the problem of whether the characteristic curves of a connection on an SO(3)-bundle on a surface are the geodesies of a Riemannian metric on the surface is studied. Some applications to non-holonomic dynamics are discussed.

scholarly journals On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Guojun Yang
Keyword(s):  
Higher Dimensions ◽  
Riemannian Metric ◽  
Dimensional Case ◽  
Finsler Metrics ◽  
Two Dimensional ◽  
Local Structures ◽  
Projectively Flat

We study a class of two-dimensional Finsler metrics defined by a Riemannian metricαand a 1-formβ. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact thatβis always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of two-dimensional (α,β)-metrics which are Douglasian, and some families of examples are given for projectively flat classes withβbeing not closed.

scholarly journals The classification of some spherically symmetric space-time metrics

1973 ◽  
Vol 8 (2) ◽  
pp. 187-190 ◽  
Author(s):  
J.M. Foyster ◽  
C.B.G. McIntosh
Keyword(s):  
Symmetric Space ◽  
Space Time ◽  
Spherically Symmetric ◽  
Symmetric Metrics

It is shown that the Petrov-Plebański classification of the trace-free Ricci tensors of some spherically symmetric metrics is invariant, contrary to an assertion by Takeno and Kitamura concerning these metrics.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

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