Finsler metrics of positive constant flag curvature on Sasakian space forms.
type: Item
instance of: scholarly article
title: Finsler metrics of positive constant flag curvature on Sasakian space forms.
zbMATH Open document ID: 1041.53045
author: Aurel Bejancu
author: Hani Reda Farran
published in: Hokkaido Mathematical Journal
publication date: 2002-01-01T00:00:00Z
review text: 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.
reviewed by: Hideo Shimada
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1809822
zbMATH Keywords: Finsler manifolds of constant flag curvature
zbMATH Keywords: Sasakian space forms
zbMATH Keywords: Randers metric
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350911875
OpenAlex ID: W2114113113
DOI: 10.14492/HOKMJ/1350911875
description: scientific article; zbMATH DE number 1809822