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A characterization of the $C$-projective vector fields on a Randers space is presented in terms of ${\bf\Xi}$-curvature. It is proved that the ${\bf\Xi}$-curvature is invariant for $C$-projective vector fields. The dimension of the algebra of the $C$-projective vector fields on an $n$-dimensional Randers space is at most $n(n+2)$. The generalized Funk metrics on the $n$-dimensional Euclidean unit ball $\mathbb{B}^n(1)$ are shown to be explicit examples of the Randers metrics with a $C$-projective algebra of maximum dimension $n(n+2)$. Then, it is also proved that an $n$-dimensional Randers space has a $C$-projective algebra of maximum dimension $n(n+2)$ if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.
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참고문헌 (22)
참고문헌 신청
H. Akbar-Zadeh / 1986 / Champ de vecteurs projectifs sur le bre unitaire / J. Math. Pures Appl 65(1):47~79
D. Bao / 2002 / Finsler metrics of constant positive curvature on the Lie group S3 / J. London Math. Soc 66(2):453~467
X. Chen / 2003 / On the ag curvature of Finsler metrics of scalar curva-ture / J. London Math. Soc 68(3):762~780
B. Najaand / 2011 / A new quantity in Finsler geometry / C. R. Math. Acad. Sci. Paris 349(1-2):81~83
B. Najaand / 2017 / Weakly stretch Finsler metrics / Publ. Math. Debrecen 91(3-4):441~454
D. Bao / 2002 / Finsler metrics of constant positive curvature on the Lie group S3 / J. London Math. Soc 66(2):453~467
X. Chen / 2003 / On the ag curvature of Finsler metrics of scalar curva-ture / J. London Math. Soc 68(3):762~780
B. Najaand / 2011 / A new quantity in Finsler geometry / C. R. Math. Acad. Sci. Paris 349(1-2):81~83
B. Najaand / 2017 / Weakly stretch Finsler metrics / Publ. Math. Debrecen 91(3-4):441~454
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