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On Generalized Douglas–Weyl(α, β)-Metrics

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1611-1620页

作者： akbar tayebi Hassan SADEGHI Department of Mathematics Faculty of Science University of Qom

In this paper, we study generalized Douglas-Weyl （α,β）-metrics. Suppose that a regular （α,β）-metric F is not of Randers type. We prove that F is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas-Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.

关键词： Generalized Douglas Weyl metric Weyl metric Douglas metric S-curvature

S-curvature of isotropic Berwald metrics

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Science China Mathematics 2008年第12期51卷 2198-2204页

作者： akbar tayebi Mehdi RAFIE-RAD Faculty of Science Department of Mathematics University of Qom Faculty of Mathematics and Computer Sciences Amirkabir University of Tecnology (Tehran Polytechnic)

Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald metric is of isotropic S-curvature. Let F = α + β be a Randers metric of isotropic Berwald curvature. Then it corresponds to a conformal vector field through navigation representation.

关键词： S-curvature isotropic Berwald metric isotropic S-curvature navigation representation 53C60 53C25

Foliations on the tangent bundle of Finsler manifolds

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Science China Mathematics 2012年第3期55卷 647-662页

作者： PEYGHAN Esmaei tayebi akbar ZHONG ChunPing Department of Mathematics Faculty of Science Arak University Arak *** Iran Department of Mathematics Faculty of Science Qom University Qom *** Iran School of Mathematical Sciences Xiamen University Xiamen 361005 China

Let M be a smooth manifold with Finsler metric F,and let T M be the slit tangent bundle of M with a generalized Riemannian metric G,which is induced by *** this paper,we prove that (i) (M,F) is a Landsberg manifold if and only if the vertical foliation F V is totally geodesic in (T M,G);(ii) letting a:= a(τ) be a positive function of τ=F 2 and k,c be two positive numbers such that c=2 k(1+a),then (M,F) is of constant curvature k if and only if the restriction of G on the c-indicatrix bundle IM (c) is bundle-like for the horizontal Liouville foliation on IM (c),if and only if the horizontal Liouville vector field is a Killing vector field on (IM (c),G),if and only if the curvature-angular form Λ of (M,F) satisfies Λ=1-a 2/R on IM (c).

关键词： Finsler manifold g-natural metrics Riemannian foliation