2) scalar curvature
标量曲率
1.
In this paper,through studying Yamabe flow,we prove that for any complete noncompact locally conformally flat manifolds,if the Ricci curvature is nonnegative,the scalar curvature is bounded and the mean value of the scalar curvature satisfies some decaying condition,then the manifold is flat.
通过Yamabe流的研究,证明了对任一完备非紧局部共形平埋的黎曼流形,若Ricci曲率非负,标量曲率有界且它的平均值满足一定衰竭条件,则此流形是平坦的。
2.
Furthermore,given a compact and boundaryless n-dimensional differentiable manifold M,we show that any pointwise C-projective change from a Berwald space (M,) to a Riemann space (M,F) is trivial if the trace of the Ricci curvature Ric of with respect to F is less or equal to the scalar curvature of F.
给定一个紧致无边的n维可微流形M,证明了:对于一个从M上的Berwald度量到Riemann度量的C射影变换,如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率,则该射影变换是平凡的。
3) constant flag curvature
常旗曲率
4) flag curvature
旗曲率
1.
In particular, we show that there exists a A-deformation perserving projective flatness for a class of Randers metric with special flag curvature.
特别,对一类具有特殊旗曲率性质的Randers度量我们证明了这类度量一定存在保持射影平坦性的λ形变。
2.
Submanifolds flag curvature and Ricci curvature of submanifolds is studied by using normal curvature, Landsberg Curvature, normal tangent Curvature, Berwald connection, and second fundamenal form in Minkowski space.
利用Ｆｉｎｓｌｅｒ法曲率Ａ、Ｌａｎｄｓｂｅｒｇ曲率Ｌｙ、法切曲率Ｆｙ、Ｂｅｒｗａｌｄ联络Ｄ以及第二基本形式Ⅱｙ，研究Ｍｉｎｋｏｗｓｋｉ空间中的子流形、子流形的旗曲率与李齐曲率。
3.
The convexity of distance function and geodesic sphere is studied by using tangent curvature and flag curvature in Finsler manifolds, and points out that the geodesic sphere is contained in the plane of Minkowski Space with complete and simply connected.
利用 Finsler流形中的切曲率和旗曲率 ,研究了距离函数与测地球的凸性 ;指出了在单连通完备 Minkowski空间中测地球正好是平面的一部
5) the horizontal flag curvature
水平旗曲率
补充资料：标量曲率
标量曲率
scalar curvature
体里州革走义.坛.碑.加re;c“”几.此翻。~二，。一，一称攀量吵半，既~流形在一点，的 Ricci张量(Ricci tensor)关于度量张量g的迹.标量曲率s(p)与Rieci曲率(Ricei eurvat眠);和截面曲率(sectional curvature)k通过公式 “(p，一，互尹(“，，一买.“(“f，“，)联系起来，这里e:，…，e。是切空间的一个规范正交基.用等价的Einstein记号，这些方程的形式为 s(夕)=夕‘，R。，二夕厅g“R*。，，这里R。和R、，，，分别是Ricci张量和曲率张量的分量，g。是度量张量的反变分量.[补注] 〔AI 1 Kobaydshi，5 .and No加zu，K.，Fo山记ations of d江ferent功1 geometry，l一2，WIlev(interse哪ee)， 1963一1969.【译注】 这里曲率张量的分量R*。，与文献[AI]中的定义相差一符号.目前大都采用IAI]的定义，因此标量曲率的公式为 S(夕)一。“R，，二。“。“R*。，，· 潘养廉译沈一兵校
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