scholarly journals Projective Vector Fields on the Cotangent Bundle with Modified Riemannian Extension

2019 ◽  
pp. 389-396
Author(s):  
Lokman BİLEN
Keyword(s):  
Cotangent Bundle ◽  
Vector Fields ◽  
Projective Vector

scholarly journals SOME NOTES ON THE MODIFIED RIEMANNIAN EXTENSION g ̃_(∇,c) ON COTANGENT BUNDLE

2020 ◽  
Vol 20 (4) ◽  
pp. 931-940
Author(s):  
HASIM CAYIR
Keyword(s):  
Cotangent Bundle ◽  
Vector Fields ◽  
Lie Derivatives ◽  
Complete And Vertical Lifts

In this paper, we define the modified Riemannian extension g ̃_(∇,c) in the cotangent bundle T^* M, which is completely determined by its action on complete lifts of vector fields. Later, we obtain the covarient and Lie derivatives applied to the modified Riemannian extension with respect to the complete and vertical lifts of vector and kovector fields, respectively.

SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE

2012 ◽  
Vol 09 (04) ◽  
pp. 1250034 ◽  
Author(s):  
M. RAFIE-RAD
Keyword(s):  
Vector Fields ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Lie Bracket ◽  
Finite Dimensional ◽  
Projective Vector ◽  
Projective Algebra ◽  
Local Characterization ◽  
Randers Metrics

The collection of all projective vector fields on a Finsler space (M, F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most [Formula: see text]. Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.

scholarly journals On Pull-Back Bundle of Tensor Bundles Defined by Projection of The Cotangent Bundle

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Furkan Yildirim
Keyword(s):  
Special Class ◽  
Cotangent Bundle ◽  
Vector Fields ◽  
Complete Lift ◽  
Tensor Bundle

AbstractUsing projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The aim of this study is to investigate complete lift of vector fields in a special class of semi-tensor bundle tM of the type (p,q). We also have a new example for good square in this work.

PROPER PROJECTIVE SYMMETRY IN SPHERICALLY SYMMETRIC STATIC SPACE–TIMES

2005 ◽  
Vol 14 (08) ◽  
pp. 1451-1463 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. AMER QURESHI
Keyword(s):  
Special Class ◽  
Vector Fields ◽  
Space Time ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Integration Techniques ◽  
Projective Vector ◽  
Static Space

A study of proper projective symmetry in spherically symmetric static space–times is given by using algebraic and direct integration techniques. It is shown that a special class of the above space–time admits proper projective vector fields.

scholarly journals SOME VECTORS FIELDS ON THE TANGENT BUNDLE WITH A SEMI-SYMMETRIC METRIC CONNECTION

2021 ◽  
pp. 669
Author(s):  
Aydin Gezer ◽  
Erkan Karakas
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Harmonic Vector ◽  
Metric Connection ◽  
Projective Vector ◽  
Harmonic Vector Fields

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic vector fields, concurrent vector fields, conformal vectorfields and projective vector fields on $TM$ with respect to thesemi-symmetric metric connection $\overline{\nabla }$ and obtain someproperties related to them.

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