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A Note on Randers Metrics of Scalar Flag Curvature

Published online by Cambridge University Press:  20 November 2018

Bin Chen  and
Lili Zhao
Bin Chen
Affiliation:
Department of Mathematics, Tongji University, Shanghai, P. R. China, 200092e-mail: [email protected]
Lili Zhao
Affiliation:
Department of Mathematics, Shanghai Jiaotong University, Shanghai, P. R. China, 200240e-mail: [email protected]
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Abstract

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Some families of Randers metrics of scalar flag curvature are studied in this paper. Explicit examples that are neither locally projectively flat nor of isotropic $S$-curvature are given. Certain Randers metrics with Einstein $\alpha $ are considered and proved to be complex. Three dimensional Randers manifolds, with $\alpha $ having constant scalar curvature, are studied.

Keywords

53B4053C60Randers metricsscalar flag curvature
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 474 - 486
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Bao, D., Robles, C., and Shen, Z., Zermelo navigation on Riemannian manifolds. J. Differential Geom. 66(2004), no. 3, 377–435.Google Scholar
[2] Bao, D. and Shen, Z., Finsler metrics of constant positive curvature on the Lie group . J. London Math. Soc. (2) 66(2002), no. 2, 453–467. http://dx.doi.org/10.1112/S0024610702003344 Google Scholar
[3] Bejancu, A. and Farran, H. R., Randers manifolds of positive constant curvature. Int. J. Math. Math. Sci. 18(2003), no. 18, 1155–1165.Google Scholar
[4] Boyer, C., Galicki, K., and Matzeu, P., On eta-Einstein Sasakian geometry. Commun. Math. Phys. 262(2006), no. 1, 177–208. http://dx.doi.org/10.1007/s00220-005-1459-6 Google Scholar
[5] Chen, B. and Zhao, L., Randers metrics of sectional flag curvature. Houston J. Math. 36(2010), no. 1, 55–67.Google Scholar
[6] Mo, X. and Shen, Z., On negatively curved Finsler manifolds of scalar curvature. Canad. Math. Bull. 48(2005), no. 1, 112–120. http://dx.doi.org/10.4153/CMB-2005-010-3 Google Scholar
[7] Shen, Z. and Yildrim, G., A characterization of Randers metrics of scalar flag curvature. manuscript, 2008. http://www.math.iupui.edu/_zshen/Research/papers/ CharacterizationOfRandersMetricsOfScalarCurvature Shen.pdf Google Scholar
[8] Shen, Y. and Yu, Y., On projectively related Randers metrics. Internat. J. Math. 19(2008), no. 5, 503–520. http://dx.doi.org/10.1142/S0129167X08004789 Google Scholar