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On projective symmetries on Finsler Spaces
- Publication Year :
- 2023
-
Abstract
- There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of $I$-invariant projective vector fields. The sub-algebra of the $C$-projective vector fields, leaving the $H$-curvature invariant, has been studied extensively. Here we show on a closed Finsler space with negative definite Ricci curvature reduces to that of Killing vector fields. Moreover, if an Einstein-Finsler space admits such a projective vector field then the flag curvature is constant. Finally, a classification of compact isotropic mean Landsberg manifolds admitting certain projective vector fields is obtained with respect to the sign of Ricci curvature.<br />25 pages
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
Flag (linear algebra)
010102 general mathematics
Space (mathematics)
Curvature
01 natural sciences
Killing vector field
Differential Geometry (math.DG)
Computational Theory and Mathematics
Projective vector field
0103 physical sciences
Homogeneous space
FOS: Mathematics
Mathematics::Metric Geometry
Vector field
Mathematics::Differential Geometry
010307 mathematical physics
Geometry and Topology
0101 mathematics
Analysis
Ricci curvature
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9acaf9de919b45ecb568e489717531fd