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A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY*

Published online by Cambridge University Press:  30 March 2012

XIAOHUAN MO
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China e-mail: moxh@pku.edu.cn
ZHONGMIN SHEN
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China e-mail: moxh@pku.edu.cn
HUAIFU LIU
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China e-mail: moxh@pku.edu.cn
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Abstract

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In this note, we study a new Finslerian quantity Ĉ defined by the Riemannian curvature. We prove that the new Finslerian quantity is a non-Riemannian quantity for a Finsler manifold with dimension n = 3. Then we study Finsler metrics of scalar curvature. We find that the Ĉ-curvature is closely related to the flag curvature and the H-curvature. We show that Ĉ-curvature gives, a measure of the failure of a Finsler metric to be of weakly isotropic flag curvature. We also give a simple proof of the Najafi-Shen-Tayebi' theorem.

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

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