Dissertation > Mathematical sciences and chemical > Mathematics > Geometry, topology > Differential geometry,integral geometry > Differential Geometry

(α, β)-metrics with Special Curvature Properties

Author WangHui
Tutor ChengXinYue
School Chongqing University
Course Basic mathematics
Keywords Finsler metric (α,β)-metric mean Cartan torsion mean Landsberg curvature
CLC O186.1
Type Master's thesis
Year 2008
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(α,β)-metrics form an important and computable class of Finsler metrics. In this paper, we obtain firstly a formula of mean Cartan torsion for (α,β)-metrics and characterize Riemann metrics among (α,β)- metrics. Further, we study the (α,β)- metrics with relatively isotropic mean Landsberg curvature and obtain a sufficient and necessary condition for the (α,β)-metrics to be of relatively isotropic mean Landsberg curvature, which generalizes the classification theorem on the weakly Landsberg (α,β)-metrics given by Chinese-American mathematician Z. Shen and B. Li released on“Science in China Series A”.

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