A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY
2012 ◽
Vol 54
(3)
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pp. 637-645
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AbstractIn 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.
2012 ◽
Vol 23
(08)
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pp. 1250084
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2013 ◽
Vol 56
(1)
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pp. 184-193
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2003 ◽
Vol 68
(03)
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pp. 762-780
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2009 ◽
Vol 61
(6)
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pp. 1357-1374
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2011 ◽
Vol 22
(07)
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pp. 925-936
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