TWO NOTABLE CLASSES OF PROJECTIVE VECTOR FIELDS

Tayebeh Tabatabeifar, Mehdi Rafie-Rad, Behzad Najafi

DOI Number
https://doi.org/10.22190/FUMI2003741T
First page
741
Last page
773

Abstract


Here, we find some necessary conditions for a projective vector field on a Randers metric to preserve the non-Riemannian quantities $\Xi$ and $H$.They are known in the contexts as the $C$-projective and $H$-projective vector fields. We find all projective vector fields of the Funk type metrics on the Euclidean unit ball $\mathbb{B}^n(1)$. 

Keywords

projective vector field; Randers metric; Funk type metrics; Euclidean unit ball.

Full Text:

PDF

References


bibitem{Az1}

{sc H. Akbar-Zadeh}, textit{Initiation to Global Finslerian Geometry}, North Holland, 2006.

bibitem{Az2}

{sc H. Akbar-Zadeh}, textit{Champs de vecteurs projectifs sur le fibré unitaire}, J. Math. Pures Appl. {bf 65} (1986) 47-79.

bibitem{B}

{sc E. Beltrami}, textit{Resoluzione del problema: riportari i punti di una superficie sopra un piano in modo che le linee geodetische vengano rappresentante da linee rette}, Ann. Mat., {bf 1(7)} (1865) 185-204.

bibitem{BM}

{sc B. Bidabad {rm and} M. Sepasi}, textit{ On a Projectively Invariant Pseudo-Distance in Finsler Geometry}, International Journal Of Geometric Methods In Modern Physics, {bf 12}(2015), 1 - 12.

bibitem{Chen}

{sc B. Chen {rm and} L. Zhao}, textit{A note on Randers metrics of scalar flag curvature}, Canad. Math. Bull., {bf 55}(2012), 474-486.

bibitem{CS}

{sc X. Cheng {rm and} Z. Shen}, textit{Finsler Geometry, An Approach via Randers Space}, Science Press, Beijing (2012).

bibitem{Matveev1}

{sc V. S. Matveev}, textit{On projective equivalence andpointwise projective relation of Randers metrics}, Int. J. Math. {bf 23}(9)(2012) 1250093 (14 pages).

bibitem{Matveev2}

{sc V. S. Matveev}, textit{Proof of projective Lichnerowicz-Obata

conjecture}, J. Differential Geom. {bf 75} (2007) 459-502,

arXiv:math/0407337.

bibitem{NT}

{sc B. Najafi {rm and} A. Tayebi}, textit{A new quantity in Finsler geometry}, C. R. Acad. Sci. Paris, Ser. I {bf 349} (1–2) (2011) 81-83.

bibitem{RR}

{sc M. Rafie-Rad}, textit{Some new characterizations of projective Randers metrics whit constant S-

curvature}, J. Geome. Phys., (2011), 7 pages.

bibitem{R2}

{sc M. Rafie-Rad}, textit{Special projective Lichnrowicz-Obata theorem for Randers spaces}, C. R. Acad.

Sci. Paris, Ser. I {bf 351} (2013), 927-930.

bibitem{Rafie}

{sc M. Rafie-Rad, B. Rezaei}, textit{On the projective algebra of Randers metrics of constant flag curvature}

SIGMA, 7 (2011) textbf{085}, 12 pages

bibitem{RSH}

{sc A. Shirafkan {rm and} M. Rafie-Rad}, textit{On the C-projective vector fields on Randers spaces}, arXiv:1811.02181v1.

bibitem{Shen}

{sc Z. Shen}, textit{On Some Non-Riemannian Quantities in Finsler Geometry}, Canad. Math. Bull. {bf 56(1)} (2013), 184--193.

bibitem{TT}

{sc A. Tayebi {rm and} T. Tabatabaeifar}, textit{ Unicorn metrics with almost vanishing {bf H}- and {bf $Xi$} curvatures},

Turkish. J. Math, {bf 41} (2017), 998--1008.

bibitem{TR}

{sc A. Tayebi {rm and} M. Razgordani}, textit{On H-curvature of $(alpha,beta)$-metrics}, Turkish J. Math, 2020,

DOI:10.3906/mat-1805-130.




DOI: https://doi.org/10.22190/FUMI2003741T

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)