Finsler metrics of positive constant flag curvature on Sasakian space forms.
This paper starts with a brief review of the basic concepts of Finsler metrics of constant flag curvature and Sasakian space form. The relationship between Randers metrics of positive constant flag curvature and Sasakian space form is pointed out first in this paper. The main result is that for any positive \(K\) there exists a Randers metric of constant flag curvature \(K\) on \(M(c)\), where \(M(c)\) is a Sasakian space form of constant \(\phi\)-sectional curvature \(c\) \((c \in (-3,1))\). Moreover, such a Randers metric is not projectively flat. Finally it has been proved that every odd dimensional sphere admits such metrics. The following papers [\textit{H. Akbar-Zadeh}, Bull. Cl. Sci., V. Sér., Acad. Roy. Belg. 74, 281--322 (1988; Zbl 0686.53020); \textit{D. Bao} and \textit{Z. Shen}, J. Lond. Math. Soc., II. Ser. 66, No. 2, 453--467 (2002; Zbl 1032.53063); \textit{S. Tanno}, Tôhoku Math. J. 21, 501--507 (1969; Zbl 0188.26801); \textit{R. Bryant}, Contemp. Math. 196, 27--41 (1996; Zbl 0864.53054) and \textit{H. Yasuda} and \textit{H. Shimada}, Rep. Math. Phys. 11, 347--360 (1977; Zbl 0362.53051)] are important references.
Finsler manifolds of constant flag curvature
scientific article; zbMATH DE number 1809822