Projective vector fields on Finsler manifolds

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.

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Affine and projective vector fields on spray manifolds

Periodica Mathematica Hungarica ◽

10.1023/b:mahu.0000038973.18653.2e ◽

2004 ◽

Vol 48 (1/2) ◽

pp. 165-179 ◽

Cited By ~ 8

Author(s):

Rezső L. Lovas

Keyword(s):

Vector Fields ◽

Projective Vector

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HORIZONTAL LAPLACIAN ON TANGENT BUNDLE OF FINSLER MANIFOLD WITH g-NATURAL METRIC

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812500612 ◽

2012 ◽

Vol 09 (07) ◽

pp. 1250061 ◽

Cited By ~ 3

Author(s):

ESMAEIL PEYGHAN ◽

AKBAR TAYEBI ◽

CHUNPING ZHONG

Keyword(s):

Tangent Bundle ◽

Vector Fields ◽

Vector Bundles ◽

Killing Vector ◽

Finsler Manifold ◽

Order Differential Operator ◽

Finsler Manifolds ◽

Scalar And Vector Fields ◽

Matsumoto Metric ◽

Weitzenböck Formula

Recently the third author studied horizontal Laplacians in real Finsler vector bundles and complex Finsler manifolds. In this paper, we introduce a class of g-natural metrics Ga,b on the tangent bundle of a Finsler manifold (M, F) which generalizes the associated Sasaki–Matsumoto metric and Miron metric. We obtain the Weitzenböck formula of the horizontal Laplacian associated to Ga,b, which is a second-order differential operator for general forms on tangent bundle. Using the horizontal Laplacian associated to Ga,b, we give some characterizations of certain objects which are geometric interest (e.g. scalar and vector fields which are horizontal covariant constant) on the tangent bundle. Furthermore, Killing vector fields associated to Ga,b are investigated.

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Fine resolution of the sheaf of germs of holomorphic projective vector fields on two dimensional protectively flat complex manifold

Bulletin Classe des sciences mathematiques et natturalles ◽

10.2298/bmat0530009m ◽

2005 ◽

Vol 131 (30) ◽

pp. 9-27

Author(s):

Olivera Milenkovic

Keyword(s):

Complex Manifold ◽

Vector Fields ◽

Two Dimensional ◽

Projective Vector ◽

Fine Resolution

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Killing vector fields on compact Finsler manifolds

Publicationes Mathematicae Debrecen ◽

10.5486/pmd.2015.6039 ◽

2016 ◽

Vol 88 (1-2) ◽

pp. 3-19

Author(s):

JINLING LI ◽

CHUNHUI QIU ◽

TONGDE ZHONG

Keyword(s):

Vector Fields ◽

Killing Vector ◽

Killing Vector Fields ◽

Finsler Manifolds

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PROPER PROJECTIVE SYMMETRY IN SPHERICALLY SYMMETRIC STATIC SPACE–TIMES

International Journal of Modern Physics D ◽

10.1142/s0218271805007255 ◽

2005 ◽

Vol 14 (08) ◽

pp. 1451-1463 ◽

Cited By ~ 5

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.

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