共查询到20条相似文献,搜索用时 78 毫秒
1.
Xiangzhi CAO 《数学年刊B辑(英文版)》2017,38(5):1071-1076
This paper deals with the p-harmonic function on a complete non-compact submanifold M isometrically immersed in an (n + k)-dimensional complete Riemannian manifold (M) of non-negative (n-1)-th Ricci curvature.The Liouville type theorem about the p-harmonic map with finite Lq-energy from complete submanifold in a partially nonnegatively curved manifold to non-positively curved manifold is also obtained. 相似文献
2.
本文主要讨论正拼挤超曲面的P-调和映射的不稳定性,从而推广了调和映射的相应结果. 相似文献
3.
在本文中我们考察从黎曼流形M到具左不变度量的齐次空间N的带位势的 p-调和映射热流,证明存在全局弱解. 相似文献
4.
Shigeo Kawai 《Geometriae Dedicata》1999,74(3):261-265
p-harmonic maps (p ' 2) between Riemannian manifolds are investigated. Some theorems of Liouville type are given for such maps when target manifolds have convex functions. 相似文献
5.
§1.IntroductionLetNn+ppbean(n+p)-dimensionalconnectedpseudo-Riemannianmanifoldofindexp.IfNn+ppiscompleteandhasconstantsection... 相似文献
6.
本文把Berard P.,do Carmo M.,Santos W.在1998年所得的结果,分别推广到局部对称的Cartan-Hadamard流形中具有常平均曲率和有限全曲率的完备超曲面,以及球面上具有平行平均曲率和有限全曲率的完备子流形. 相似文献
7.
讨论非齐次p-调和映射方程组弱驻点解的内部正则性,证明了弱驻点解满足拟单调不等式,得到了弱驻点解梯度的Holder连续性。 相似文献
8.
Huang Chengchao 《数学年刊B辑(英文版)》1982,3(2):169-178
The Properties of submanifolds in a Bochner-Kaehler manifold have been studied
mainly in the cases that the submanifolds are totally real by Yano, K., Houh, 0. S. and others.
The main purpose of the present paper is to study whether the condition for the
submanifold to be totolly real in their theorems is necessary, and to prove some
theorems which are analogous to those mentioned above.
A submanifold M^n of Kaehlerian manifold M^2m is called totally real or antiinvariant,if each tangent space of M^n is mapped into the normal space by the complex structure $\[{F_{\nu \mu }}\]$ of M^2m. Similarly, a submanifold M^n of Kaehlerian manifold M^2m is called anti-in variant with respect to L', if each tangent space of M^n is mapped into the normal space by the operator L' of M^2m.
We obtain:
(1) A necessary and sufficient condition for a totally umbilical submanifold M^n,
n>3, in a Boohner-Kaehler manifold M^2m to be conformally flat is that the submanifold M^n is either a totally real submanifold or an anti-invariant submanifold with respect to L'.
(2) Let M^n be the submanifold immersed in a Boohner-Kaehler manifold M^2m.
If each tangent vector of M^n is Ricci principal direction and Ricci principal curvature $\[{\rho _h}\]$ does not equal $[\frac{{\tilde K}}{{4(m + 1)}}\]$ , then the anti-invariant submanifold with respect to L^' coincides with the totally real submanifold.
(3) Let M^n be a totally umbilical submanifold immersed in a Boohner-Kaehler
manifold M^2m If M^n is a totally real submanifold or an anti-invariant submanifold,then the sectional curvature of Mn is given by
$[\rho (u,v) = \frac{1}{8}(\tilde K(u) + \tilde K(v)) + \sum\limits_{x = n + 1}^{2m} {{H^2}} ({e_x})\]$(A)
where H(e_x) =H_x. Conversely, if the sectional curvature of M^n satisfying the condition mentioned in (2) is given by (A) for any two orthonormal tangent vectors u^\alpha and $v^\alpha$ then M^n is a totally real submanifold. 相似文献
9.
Shen yibing 《数学年刊B辑(英文版)》1984,5(4):625-632
This paper gives some sufficient conditions for a compact submanifold with nonnegative sectional curvature in a space form to be totally umbilical. In particular, for a compact submanifold M with flat normal bundle, if the scalar curvature is proportional to the mean curvature everywhere, then M is totally umbilical or the Riemannian product of several totally umbilical constantly curved submanifolds. 相似文献
10.
We show that mean curvature flow of a compact submanifold in a complete Riemannian manifold cannot form singularity at time
infinity if the ambient Riemannian manifold has bounded geometry and satisfies certain curvature and volume growth conditions. 相似文献
11.
We give a proof of asymptotic Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Lipschitz continuity and Harnack's inequality for p-harmonic functions in the case p > 2. The proof avoids classical techniques like Moser iteration, but instead relies on suitable choices of strategies for the stochastic tug-of-war game. 相似文献
12.
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
13.
周春琴 《数学物理学报(A辑)》1998,(1)
研究了与P-Laplace算子对映的铁磁链系统的Landau-Lifshitz方程,证明了该方程的从m(m≥3)维紧流形M(不带边界)映射到R3中的单位球面S2上的整体弱解的存在性;建立了p-调和映射理论与该方程的联系. 相似文献
14.
Gregory J. Galloway 《manuscripta mathematica》1981,35(1-2):209-219
Varying the situation considered in Myers theorem, we show, via standard index form techniques, that a complete Riemannian manifold which admits a compact minimal submanifold is necessarily compact, provided a suitable curvature object is positive on the average along the geodesies issuing orthogonally from the minimal submanifold. By slightly recasting this result, one establishes the nonexistence of compact minimal submanifolds (in particular, closed geodesies) in complete noncompact manifolds which obey an appropriate curvature condition. A generalization of a result of Tipler concerning the occurrence of zeros of solutions to the scalar Jacobi equation is also obtained. 相似文献
15.
Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng. 相似文献
16.
该文证明了de Sitter空间中具有平行平均曲率向量的常数量曲率完备类空子流形,如果其法联络是平坦的,且M的截面曲率小于0,或M的第二基本形式模长平方‖σ‖相似文献
17.
18.
We prove explicit lower bounds for the capacity of annular domains
of minimal submanifolds P
m
in ambient Riemannian spaces N
n
with
sectional curvatures bounded from above. We characterize the situations
in which the lower bounds for the capacity are actually attained.
Furthermore we apply these bounds to prove that Brownian motion
defined on a complete minimal submanifold is transient when the ambient
space is a negatively curved Hadamard-Cartan manifold. The
proof stems directly from the capacity bounds and also covers the case
of minimal submanifolds of dimension m > 2 in Euclidean spaces. 相似文献
19.
We prove that a Lagrangian submanifold passes through each point of a symplectic manifold in the direction of arbitrary Lagrangian plane at this point. Generally speaking, such a Lagrangian submanifold is not unique; nevertheless, the set of all such submanifolds in Hermitian extension of a symplectic manifold of dimension greater than 4 for arbitrary initial data contains a totally geodesic submanifold (which we call the s-Lagrangian submanifold) iff this symplectic manifold is a complex space form. We show that each Lagrangian submanifold in a complex space form of holomorphic sectional curvature equal to c is a space of constant curvature c/4. We apply these results to the geometry of principal toroidal bundles. 相似文献
20.
Summary Let T(M) be the tangent bundle over a Finslerian manifold M of n-dimension endowed with the Cartan connection ∇. One makes
T(M) into a 2n dimensional affinely connected manifold by assigning a connection ∇c to T(M). The cross-section
of a vector field V defined in M reveals in T(M) an n-dimensional submanifold and its geometry is developed by means of the
affine subspace theory and of the affine collineations in the base Finsler manifold.
This work was supported by the National Research Council of Canada, 1970–1971, A-4037.
Entrata in Redazione il giorno 8 maggio 1971. 相似文献