1) Riemannian manifold
Riemann 流形
1.
We obtained a vanishing theorem for L~2 geodesic vector fields on complete Riemannian manifolds together with a condition that Einstein manifold is isometric to a sphere.
本文得到完备 Riemann 流形上 L~2测地向量场的一个消没定理,同时给出Einstein 流形与一球面等距的一个条件。
2) Riemann manifold
Riemann流形
1.
Euler equation of weakly harmonic maps from high dimension Riemann manifold to homogeneous space;
高维Riemann流形到齐次空间弱调和映射的Euler方程
2.
In this paper,the geometry of the 2-harmonic hypersurfaces in Riemann manifold is studied,and we obtained two sufficient condictions under which a 2-harmonic hypersurface turns into a minimal hypersurface.
研究了Riemann流形中的2-调和超曲面,给出了2-调和超曲面成为极小的两个充分条件。
3.
Let M be a compact n-dimensional Riemann manifold, RicM≥n-1, Let d denote the diameter of M.
M为紧致n维Riemann流形 ,Ricci曲率具有正下界n- 1 ,d是M的直径 ,本文证明了其Laplace算子的第一特征值λ1≥ π2d2 + n- 12 。
3) Riemannian manifold
Riemann流形
1.
Weighted Laplacian operator on Riemannian manifolds;
Riemann流形上的加权Laplace算子
2.
By deriving sharp gradient estimates for the positive solutions of the heat equation and deducing some Harnack type inequalities, we obtain some quantitative estimates of the lower bounds for heat kernels and higher eigenvalues on Riemannian manifold with Ric (M)≥-K (K>0).
对Ricci曲率具负下界的紧Riemann流形,本文获得了热方程正解优化的梯度估计及Harnack不等式,证明了高阶特征值下界定量估计的猜想。
3.
Let A be the Laplace-Beltrami operator on a Riemannian manifold M.
设Δ是Riemann流形M上的Laplace-Beltrami算子。
4) Quasi Riemann manifold
准Riemann流形
5) compact Riemann manifolds
紧Riemann流形
补充资料：Riemann流形
Riemann流形
Riemannian manifold
Rieltlann流形【Ri~.吐叨，诩丽创d;入M阴。即M”。-r006pa3He」 带有Rien.lul度最(RienlanIUall能tric)的微分流形(山价rentinble rnan而kl).本质上，RieIT以nn流形与R记n栩团口空间(Riernonltian sPace)是相同的. M.H.B成那xoBcK戒撰播养廉译
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