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On Projectively Flat (α, β)-metrics

Published online by Cambridge University Press:  20 November 2018

Zhongmin Shen
Zhongmin Shen*
Affiliation:
Center for Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang Province 310027, P.R. China e-mail: zshen@math.iupui.edu
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Abstract

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The solutions to Hilbert's Fourth Problem in the regular case are projectively flat Finsler metrics. In this paper, we consider the so-called $\left( \alpha ,\,\beta\right)$ -metrics defined by a Riemannian metric $\alpha$ and a 1-form $\beta$ , and find a necessary and sufficient condition for such metrics to be projectively flat in dimension $n\,\ge \,3$ .

Keywords

53B4053C60

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009, pp. 132 - 144
Copyright
Copyright © Canadian Mathematical Society 2009

References

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