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On Some Explicit Constructions of Finsler Metrics with Scalar Flag Curvature

Published online by Cambridge University Press:  20 November 2018

Xiaohuan Mo  and
Changtao Yu
Xiaohuan Mo*
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
Changtao Yu*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
*
[email protected]
[email protected]
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Abstract

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We give an explicit construction of polynomial (of arbitrary degree) $(\alpha ,\,\beta )$-metrics with scalar flag curvature and determine their scalar flag curvature. These Finsler metrics contain all nontrivial projectively flat $(\alpha ,\,\beta )$-metrics of constant flag curvature.

Keywords

58E20Finsler metricscalar curvatureprojective flatness
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 6 , 14 December 2010 , pp. 1325 - 1339
Copyright
Copyright © Canadian Mathematical Society 2010

Footnotes

This work is supported by the National Natural Science Foundation of China 10471001.

References

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