共查询到18条相似文献,搜索用时 125 毫秒
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完备Riemann流形之共轭点 总被引:14,自引:0,他引:14
本文证明了具非负曲率完备Riemann测地线为无共轭点测地线的充要条件;并由此证明了若该流形上的截面含有一无共轭点测地线的切向量,则其对应的截曲率为零. 相似文献
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具非负Ricci曲率和严格(1+δ)阶体积增长的三维流形 总被引:1,自引:1,他引:0
本文研究了三维完备非紧具非负Ricci曲率的黎曼流形的几何拓扑性质.通过对流形本身与流形的万有覆盖空间体积增长阶的比较,证明了对具非负Ricci曲率和严格(1+δ)阶体积增长的三维完备非紧的黎曼流形是可缩的. 相似文献
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可定向的具非负曲率完备非紧黎曼流形 总被引:5,自引:0,他引:5
本文研究了具非负曲率完备非紧黎曼流形的一些几何性质,包括闭测地线,体积等.证明了核心的余维数为奇数的可定向具非负曲率完备非紧黎曼流形在其核心的任一法测地线均为射线的条件下可等距分裂为R×N,其中N为低一维的流形. 相似文献
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具非负曲率完备非紧曲面的几何性质 总被引:1,自引:0,他引:1
本文证明了单连通完备非紧具非负曲率之曲面的任一测地线γ:[0,+∞)→M均趋于∞处这一几何性质,指出了一般的高维流形不具有此性质.本文还证明了单连通完备非紧具非负曲率的曲面的割迹与第一共轭轭迹是一致的;并且讨论了一般高维流形的共轭点与测地线的关系. 相似文献
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舒世昌 《纯粹数学与应用数学》1995,11(A01):8-12
文[1]的重要结果推广到了环绕空间是局部对称共形平坦的情形,得到了这种空间中极小子流形截面曲率非负时,Ricci曲率应满足的条件,做为应用,得到了比文[1]中结果更强的一个几何结果。 相似文献
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We prove new ergodic theorems in the context of infinite ergodic theory, and give some applications to Riemannian and Kähler manifolds without conjugate points. One of the consequences of these ideas is that a complete manifold without conjugate points has nonpositive integral of the infimum of Ricci curvatures, whenever this integral makes sense. We also show that a complete Kähler manifold with nonnegative holomorphic curvature is flat if it has no conjugate points. 相似文献
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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
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In this paper, we prove the almost Schur theorem, introduced by De Lellis and Topping, for the Riemannian manifold M of nonnegative Ricci curvature with totally geodesic boundary. Examples are given to show that it is optimal when the dimension of M is at least 5. We also prove that the almost Schur theorem is true when M is a 4-dimensional manifold of nonnegative scalar curvature with totally geodesic boundary. Finally we obtain a generalization of the almost Schur theorem in all dimensions only by assuming the Ricci curvature is bounded below. 相似文献
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Quo-Shin Chi 《Annals of Global Analysis and Geometry》1991,9(3):197-204
Using the twistor theory on quaternionic Kaehler manifolds and some recent results on Blaschke manifolds and compact manifolds whose holonomy group is Spin (7), we prove that a Blaschke manifold of nonnegative scalar curvature whose holonomy group is exceptional is isometric to a projective space. 相似文献
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Maria Helena Noronha 《Geometriae Dedicata》1993,47(3):255-268
In this paper we study some compact locally conformally flat manifolds with a compatible metric whose scalar curvature is nonnegative, and in particular with nonnegative Ricci curvature. In the last section we study such manifolds of dimension 4 and scalar curvature identically zero. 相似文献
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Seong-Hun Paeng 《Proceedings of the American Mathematical Society》2003,131(8):2577-2583
Gromov conjectured that the fundamental group of a manifold with almost nonnegative Ricci curvature is almost nilpotent. This conjecture is proved under the additional assumption on the conjugate radius. We show that there exists a nilpotent subgroup of finite index depending on a lower bound of the conjugate radius.
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YONGFAN Zheng 《Geometriae Dedicata》1997,67(3):295-300
Let M be a compact orientable submanifold immersed in a Riemannian manifold of constant curvature with flat normal bundle. This paper gives intrinsic conditions for M to be totally umbilical or a local product of several totally umbilical submanifolds. It is proved especially that a compact hypersurface in the Euclidean space with constant scalar curvature and nonnegative Ricci curvature is a sphere. 相似文献