Geodesic
A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY*
Glasgow mathematical journal, Tome 54 (2012) no. 3, pp. 637-645

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DOI

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.
DOI : 10.1017/S0017089512000225
Mots-clés : 58E20 
MO, XIAOHUAN; SHEN, ZHONGMIN; LIU, HUAIFU. A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY*. Glasgow mathematical journal, Tome 54 (2012) no. 3, pp. 637-645. doi: 10.1017/S0017089512000225
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     title = {A {NEW} {QUANTITY} {IN} {RIEMANN-FINSLER} {GEOMETRY*}},
     journal = {Glasgow mathematical journal},
     pages = {637--645},
     year = {2012},
     volume = {54},
     number = {3},
     doi = {10.1017/S0017089512000225},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000225/}
}
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