共查询到20条相似文献,搜索用时 62 毫秒
1.
中曲率大于零的非凸曲面 总被引:1,自引:1,他引:0
本文研究了曲面的曲率问题.利用积分几何方法和旋转曲面性质,构造出一个欧氏空间R3中紧致光滑的中曲率H大于零的非凸曲面,并得到了关于紧致光滑曲面曲率的几个不等式. 相似文献
2.
设Mn是复射影空间CPn+p/2中具有平坦法丛的一般极小子流形.该文研究了这种子流形的曲率性质与几何性质之间的关系.运用活动标架法,得到关于Ricci曲率和第二基本形式模长的刚性定理,完善了已有文献的相关结果.此外,该文还得到具有平坦法丛的一般子流形一个重要性质. 相似文献
3.
邓义华 《数学的实践与认识》2010,40(23)
讨论了具有相对迷向平均Landsberg曲率的度量的一些几何性质.证明了任一闭的具有负旗曲率与相对迷向平均Landsberg曲率的流形一定是Riemann流形. 相似文献
4.
得到了具有常m阶Schouten曲率与两个不同Schouten主曲率(或者等价地,两个不同Ricci上曲率)的完备局部共形平坦Riemann流形的分类结果.作为应用,得到了若干Schouten张量的pinching性质. 相似文献
5.
吴炳烨 《数学年刊A辑(中文版)》2011,32(1):71-82
得到了具有常m阶Schouten曲率与两个不同Schouten主曲率(或者等价地,两个不同Ricci主曲率)的完备局部共形平坦Riemann流形的分类结果.作为应用,得到了若干Schouten张量的pinching性质. 相似文献
6.
本文研究了双曲空间形式中等距浸入的紧致无边超曲面的全脐性质和高阶平均曲率.利用高阶平均曲率积分估计的方法,获得了一个新的定理,改进了这个研究方向上有关的最近结果. 相似文献
7.
本文研究局部有限图上的曲率维数不等式CD(n,K)的若干等价性质,包括梯度估计、Poincaré不等式和逆Poincaré不等式.还得到了局部有限图上的修正曲率维数不等式CDE′(∞,K)的其中一个等价性质,即梯度估计. 相似文献
8.
9.
本文研究正曲率空间形式S~(n+1)(c)(c0)中紧致的闭的等距浸入超曲面M~n的全脐性质和高阶平均曲率,所得结果改进和推广了这方面最近有关定理. 相似文献
10.
11.
M.-L. Labbi 《Geometriae Dedicata》2004,108(1):205-217
In this paper we study positive Einstein curvature which is a condition on the Riemann curvature tensor intermediate between
positive scalar curvature and positive sectional curvature. We prove some constructions and obstructions for positive Einstein
curvature on compact manifolds generalizing similar well known results for the scalar curvature. Finally, because our problem
is relatively new, many open questions are included. 相似文献
12.
We establish a nice orthonormal frame field on a closed surface minimally immersed in a unit sphere Sn, under which the shape operators take very simple forms. Using this frame field, we obtain an interesting property K + K~N= 1 for the Gauss curvature K and the normal curvature K~N if the Gauss curvature is positive. Moreover, using this property we obtain the pinching on the intrinsic curvature and normal curvature, the pinching on the normal curvature, respectively. 相似文献
13.
A. J. Tromba 《manuscripta mathematica》1986,56(4):475-497
A formula for the sectional curvature of Teichmüller space with respect to the Weil-Petersson metric is derived in terms of the Laplace-Beltrami operator on functions. It will be shown that the sectional curvature as well as the holomorphic sectional curvature and Ricci curvature are negative. Bounds on the holomorphic and the Ricci curvature are given. 相似文献
14.
Laurent Veysseire 《Comptes Rendus Mathematique》2010,348(23-24):1319-1322
Most known lower bounds on the spectral gap of the Laplacian using Ricci curvature are based on the infimum of the Ricci curvature, and can be really poor when the Ricci curvature is large everywhere but on a small subset on which it is small. Here we show that the harmonic mean of the Ricci curvature is a lower bound on the spectral gap of the Laplacian, which partially solves the problem (unfortunately, we have to assume that the Ricci curvature is everywhere nonnegative). 相似文献
15.
We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. For (α,β)-metrics on manifold of dimension greater than 2, if the mean Landsberg curvature and the Berwald scalar curvature both vanish, then the Berwald curvature also vanishes. 相似文献
16.
Zhang Zonglao 《Proceedings Mathematical Sciences》2005,115(3):309-318
This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature.
We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results
for complete solutions of scalar curvature equation. 相似文献
17.
许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战. 相似文献
18.
In this paper we are concerned with the structure of curves on surfaces whose geodesic curvature is a large constant. We first discuss the relation between closed curves with large constant geodesic curvature and the critical points of Gauss curvature. Then, we consider the case where a curve with large constant geodesic curvature is immersed in a domain which does not contain any critical point of the Gauss curvature. 相似文献
19.
Zhongmin Qian 《Bulletin des Sciences Mathématiques》2009,133(2):145-168
In this paper we consider Hamilton's Ricci flow on a 3-manifold with a metric of positive scalar curvature. We establish several a priori estimates for the Ricci flow which we believe are important in understanding possible singularities of the Ricci flow. For Ricci flow with initial metric of positive scalar curvature, we obtain a sharp estimate on the norm of the Ricci curvature in terms of the scalar curvature (which is not trivial even if the initial metric has non-negative Ricci curvature, a fact which is essential in Hamilton's estimates [R.S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255-306]), some L2-estimates for the gradients of the Ricci curvature, and finally the Harnack type estimates for the Ricci curvature. These results are established through careful (and rather complicated and lengthy) computations, integration by parts and the maximum principles for parabolic equations. 相似文献
20.
Qi S. Zhang 《Mathematische Annalen》2000,316(4):703-731
By establishing an optimal comparison result on the heat kernel of the conformal Laplacian on open manifolds with nonnegative
Ricci curvature, (a) we show that many manifolds with positive scalar curvature do not possess conformal metrics with scalar
curvature bounded below by a positive constant; (b) we identify a class of functions with the following property: If the manifold
has a scalar curvature in this class, then there exists a complete conformal metric whose scalar curvature is any given function
in this class. This class is optimal in some sense; (c) we have identified all manifolds with nonnegative Ricci curvature,
which are “uniformly” conformal to manifolds with zero scalar curvature. Even in the Euclidean case, we obtain a necessary
and sufficient condition under which the main existence results in [Ni1] and [KN] on prescribing nonnegative scalar curvature
will hold. This condition had been sought in several papers in the last two decades.
Received: 11 November 1998 / Revised: 7 April 1999 相似文献