2) S-curvature
S-曲率
1.
On the Exponential Metrics with Isotropic S-curvature;
具有迷向S-曲率的指数度量
2.
Two kinds of(α,β)-Metrics with Isotropic S-curvature;
具有迷向S-曲率的两类(α,β)-度量
3.
On the S-curvature of Some (α,β)-metrics;
关于(α,β)-度量的S-曲率
4) surface of constant curvature
常曲率曲面
5) quasi-constant curvature
拟常曲率
1.
Let Nn+p be an n+p-dimensional locally symmetric complete quasi-constant curvature Riemannian manifold and Mn be an n-dimensional compact sub-manifold in Mn+p with paralleled mean curvature vector.
设Nn+p是n+p维局部对称完备的拟常曲率黎曼流形。
2.
This paper presents a necessary and sufficient condition that the recurrent hypersurface M in a Riemannian space with quasi-constant curvature is locally symmetric,and shows that the complete irreducible birecurrent hypersurface M in a Riemannian space with quasi-constant curvature is recurrent if the generating element of N is a normal vector field or pungent vector field of M.
给出拟常曲率空问Ｎ中循环超曲面Ｍ局部对称的一个充要条件，并且证明若拟常曲率空间Ｎ的生成元是其完备不可约双循环超曲面Ｍ的法向量或切向量，则Ｍ是循环的。
3.
We generalize the two theorems of submanifolds in constant curvature manifolds to the external sphere mani-folds in quasi-constant curvature.
本文将常曲率流形的子流形的两个定理推广到拟常曲率外围流形的情形,得到了全脐的一个充分条件。
6) constant curvature
常曲率
1.
The authors study the property of a class of(α,β)-metrics F in which β is parallel with respect to Riemann metric α and Riemann metric α is of constant curvature,and it is obtained that F is flat-parallel metric or conformally related to Riemann metric α.
研究一类β关于α是平行的并且Riemann度量α具有常曲率的(α,β)-度量F所具有的一些性质,证明了F要么是平坦平行度量,要么是与Riemann度量α共形相关的度量。
2.
In the present paper, the authors first study Finsler spaces satisfying L_ :0+K(x, y)F2C=0, show that it must be of constant curvature, and obtain some interesting conclusions.
证明了它一定具有常曲率,并得到一些有趣的相关结论,解决了下述著名定理的反问题:具有常曲率λ的芬斯勒空间一定满足L:0+λF2C=0。
3.
The purpose of this paper is to give some conditions which a Finsler space of constant curvature remains to be a Finsler space of constant curvature by a geodesic mapping of Finsler space.
常曲率Finsler、局部Minkowski空间的测地映射是Finsler几何的重要问题,本文首先获得了在 Finsler空间测地映射下,常曲率Finsler空间保持不变的充要条件并推导了局部 Minkowski空间经 Finsler空间的测地映射仍然是局部Minkowski空间的充要条件,此外还推导出在测地映射下,Berwald空间等保持不变的新的充要条件。
补充资料：曲率
平面曲线的曲率就是针对曲线上某个点的切线方向角对弧长的转动率，通过微分来定义，表明曲线偏离直线的程度。曲率越大，表示曲线的弯曲程度越大。
k=lim|δα/δs|，δs趋向于0的时候，定义k就是曲率。
曲率的倒数就是曲率半径。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条