排序方式: 共有27条查询结果,搜索用时 15 毫秒
1.
Gerard A. Venema 《Topology and its Applications》1998,90(1-3):197-210
A core of a (noncompact) manifold is a submanifold with the property that the inclusion of the submanifold into the manifold is a homotopy equivalence. It is shown by example that a manifold may fail to contain a compact core even though the manifold has the homotopy type of a finite complex. 相似文献
2.
子流形与拓扑球面定理 总被引:1,自引:0,他引:1
本文建立了球面Sn p(c) (c>0 )中的完备子流形的一个拓扑球面定理 ,结果表明完备子流形的拓扑是受其内在和外在曲率不变量满足的某些条件所影响的 相似文献
3.
本利用几何不等式和曲率估计的方法,证明了黎曼流形N^n+p,上的具有平行平均曲率的紧子流形M^n上的一个拼挤定理。若N上的截曲率KN满足- 1≤ KN≤δ≤0,且‖S- nH2‖n/2, ‖ S-nH^2‖n/n-s满足一些不等式,则δ= - 1。 相似文献
4.
Vladimir Rovenski 《Geometriae Dedicata》2006,121(1):187-203
The paper continues our (in collaboration with A. Borisenko [J. Differential Geom. Appl. 20 p., to appear]) discovery of the new classes of $(k,\varepsilon)The paper continues our (in collaboration with A. Borisenko [J. Differential Geom. Appl. 20 p., to appear]) discovery of the
new classes of
-saddle,
-parabolic, and
-convex submanifolds (
). These are defined in terms of the eigenvalues of the 2nd fundamental forms of each unit normal of the submanifold, extending
the notion of k-saddle, k-parabolic, k-convex submanifolds (
). It follows that the definition of
-saddle submanifolds is equivalent to the existence of
-asymptotic subspaces in the tangent space. We prove non-embedding theorems of
-saddle submanifolds, theorems about 1-connectedness and homology groups of these submanifolds in Riemannian spaces of positive
(sectional or qth Ricci) curvature, in particular, spherical and projective spaces. We apply these results to submanifolds with ‘small’ normal
curvature,
, and for submanifolds with extrinsic curvature
(resp., non-positive) and small codimension, and include some illustrative examples. The results of the paper generalize
theorems about totally geodesic, minimal and k-saddle submanifolds by Frankel; Borisenko, Rabelo and Tenenblat; Kenmotsu and Xia; Mendon?a and Zhou.
相似文献
5.
§1.IntroductionLetMbeann-dimensionalclosedminimalyimmersedsubmanifoldintheunitsphereSn+p,Sthesequreofthelengthofthesecondfund... 相似文献
6.
SkewCRSubmanifoldsofaSasakianManifoldLiuXimin(刘西民)(DepartmentofMathematics,NankaiUniversity,Tianjin,300071)LiangXiquan(梁希泉)(I... 相似文献
7.
A. Largillier 《Applied Mathematics Letters》1996,9(6):79-84
The goal of this paper is to obtain optimal first order bounds for absolute and relative errors of unitary and Hermitian factors of some commonly used matrix factorizations. We have chosen the strong derivative calculus approach and we have expressed the factors as a differentiable function of the data but since these expressions define the functions implicitly, the inverse function theorem plays a central role in finding the Jacobian matrix. Then, first order bounds are deduced by means of the mean value theorem for the derivatives. We either improve or generalize some of the bounds proposed by Bhatia [1], Stewart [2], and Sun [3]. 相似文献
8.
本文利用一个类似于Cheng和Yau引进的微分算子的新微分算子,得到了单位球面中常数量率的紧致子流形的一个刚性结果. 相似文献
9.
We obtain upper bounds for the Steklov eigenvalues of a smooth, compact, n-dimensional submanifold M of Euclidean space with boundary Σ that involve the intersection indices of M and of Σ. One of our main results is an explicit upper bound in terms of the intersection index of Σ, the volume of Σ and the volume of M as well as dimensional constants. By also taking the injectivity radius of Σ into account, we obtain an upper bound that has the optimal exponent of k with respect to the asymptotics of the Steklov eigenvalues as . 相似文献
10.