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91.
In this paper, the authors present a method to construct the minimal and H-minimal Lagrangian submanifolds in complex hyperquadric Qn from submanifolds with special properties in odd-dimensional spheres. The authors also provide some detailed examples. 相似文献
92.
SUN He-jun WU Bao-qiang.Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China .Department of Mathematics Xuzhou Normal University Xuzhou China 《数学季刊》2004,19(1):6-15
We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form. 相似文献
93.
94.
Austere submanifolds and arid submanifolds constitute respectively two different classes of minimal submanifolds in finite dimensional Riemannian manifolds. In this paper we introduce the concepts of these submanifolds into a class of proper Fredholm (PF) submanifolds in Hilbert spaces, discuss their relation and show examples of infinite dimensional austere PF submanifolds and arid PF submanifolds in Hilbert spaces. We also mention a classification problem of minimal orbits in hyperpolar PF actions on Hilbert spaces. 相似文献
95.
In contrast to an infinite family of explicit examples of two-dimensional p-harmonic functions obtained by G. Aronsson in the late 80s, there is very little known about the higher-dimensional case. In this paper, we show how to use isoparametric polynomials to produce diverse examples of p-harmonic and biharmonic functions. Remarkably, for some distinguished values of p and the ambient dimension n this yields first examples of rational and algebraic p-harmonic functions. Moreover, we show that there are no p-harmonic polynomials of the isoparametric type. This supports a negative answer to a question proposed in 1980 by J. Lewis. 相似文献
96.
双曲空间Hn+p(-1)中具常数量曲率的完备子流形 总被引:3,自引:0,他引:3
设Mn是Hn p(-1)中具有常标准数量曲率的n维完备子流形,本文证明了这种完备子流形的某些内蕴刚性定理和分类定理,并对超曲面的情形进行了研究. 相似文献
97.
98.
1973年,H.B.Lawson和J.Simons猜想,在任何紧致,单连通,1/4-pinched黎曼流形中,不存在稳定积分流,本文研究全拟脐子流形中稳定积分流的不存在性,证明了在一定几何条件下,这类流形中不存在稳定积分流,由此得到几个同调群的消设定理,所得结果表明,Lawson-Simons猜想对于拟脐超曲面和某些全拟脐子流形是对的。 相似文献
99.
Let be an n-dimensional compact, possibly with boundary, submanifold in an (n + p)-dimensional space form R
n+p
(c). Assume that r is even and , in this paper we introduce rth mean curvature function S
r
and (r + 1)-th mean curvature vector field . We call M to be an r-minimal submanifold if on M, we note that the concept of 0-minimal submanifold is the concept of minimal submanifold. In this paper, we define a functional
of , by calculation of the first variational formula of J
r
we show that x is a critical point of J
r
if and only if x is r-minimal. Besides, we give many examples of r-minimal submanifolds in space forms. We calculate the second variational formula of J
r
and prove that there exists no compact without boundary stable r-minimal submanifold with in the unit sphere S
n+p
. When r = 0, noting S
0 = 1, our result reduces to Simons’ result: there exists no compact without boundary stable minimal submanifold in the unit
sphere S
n+p
.
相似文献
100.
Leng Yan Xu Hongwei 《高校应用数学学报(英文版)》2007,22(2):153-162
A rigidity theorem for oriented complete submanifolds with parallel mean curvature in a complete and simply connected Riemannian (n p)-dimensional manifold Nn p with negative sectional curvature is proved. For given positive integers n(≥ 2), p and for a constant H satisfying H > 1 there exists a negative number τ(n,p, H) ∈ (-1, 0) with the property that if the sectional curvature of N is pinched in [-1, τ(n,p, H)], and if the squared length of the second fundamental form is in a certain interval, then Nn p is isometric to the hyperbolic space Hn p(-1). As a consequence, this submanifold M is congruent to Sn(1/ H2-1) or theVeronese surface in S4(1/√H2-1). 相似文献