【摘要】：本文主要圍繞芬斯勒幾何中一類重要的幾何量——Landsberg曲率展開了深入研究。首先,我們對(duì)射影平坦的(α,β)-度量展開了研究,并分類刻畫了射影平坦的Berwald(α,β)-度量和射影平坦的弱Landsberg(α,β)-度量以及射影平坦且具有相對(duì)迷向平均Landsberg曲率的(α,β)-度量。其次,我們研究了具有相對(duì)迷向平均Landsberg曲率(即J+c(x)FI=0)的閉的芬斯勒流形,并證明了若c(x)在流形上恒為正或恒為負(fù),則該流形一定是黎曼流形。此外,本文研究了具有迷向平均Berwald曲率的芬斯勒度量F,并給出了F具有殆迷向S-曲率的一個(gè)充分條件。最后,與他人合作,本文給出了具有弱迷向旗曲率的芬斯勒度量所滿足的一個(gè)偏微分方程組;還給出了具有標(biāo)量旗曲率且具有常數(shù)平均Berwald曲率的芬斯勒度量的旗曲率K所滿足的一個(gè)恒等式。
[Abstract]:This paper focuses on a class of important geometric quantities in Finsler geometry, Landsberg curvature. Firstly, we study the projective flat (偽, 尾) -metric, and characterize the projective flat Berwald (偽, 尾) -metric and the projectively flat weakly Landsberg (偽, 尾) -metric and the projective flat (偽, 尾) -metric with the relative isotropic average Landsberg curvature. Secondly, we study the closed Fensler manifold with the relative isotropic mean Landsberg curvature (that is, J c (x) FI0), and prove that if c (x) is always positive or negative on the manifold, then the manifold must be Riemannian manifold. In addition, we study the Fensler metric F with isotropic mean Berwald curvature, and give a sufficient condition for F to have almost isotropic S-curvature. Finally, in cooperation with others, we give a partial differential equation system of Fensler metric with weak isotropic flag curvature. An identity of the flag curvature K of the Fensler metric with scalar flag curvature and constant average Berwald curvature is also given.
【學(xué)位授予單位】：重慶理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O186.1

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相關(guān)期刊論文 前6條

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本文編號(hào)：2135269