具有迷向S-曲率的Douglas(α,β)-度量

Douglas (α,β)-metrics with isotropic S-curvature

研究具有迷向S-曲率的Douglas(α,β)-度量F=αφ(β/α),其中α=aij(x)yiyj～(1/2)为黎曼度量,β=bi(x)yi为流形上的1-形式.得到其为具有迷向S-曲率的Douglas度量的充要条件是β关于α是平行的.进一步,完全地分类了局部射影平坦且具有迷向S-曲率的(α,β)-度量.

Douglas （α,β）-metrics F= αφ（β/α） with isotropic S-curvature were studied, where α =√aij （x）yiyj was a Riemannian metric and β=bi （x）yi was a 1-form on the manifold. It was found that the sufficient and necessary condition for Douglas metrics with isotropic S-curvature would be β being parallel with respect to a. Further, locally projectively flat （α,β）-metrics with isotropic S-curvature were classified completely.