共查询到20条相似文献,搜索用时 31 毫秒
1.
We show that a conformal mapping between Riemannian manifolds of the same dimension n ≥ 3 is biharmonic if and only if the gradient of its dilation satisfies a certain second-order elliptic partial differential
equation. On an Einstein manifold solutions can be generated from isoparametric functions. We characterise those semi-conformal
submersions that are biharmonic in terms of their dilation and the fibre mean curvature vector field.
相似文献
2.
本文利用复射影空间到欧氏空间的第一标准嵌入,对于复射影空间的子流形建立了一种广义的Gauss映照,并给出了这种广义的Gau8s映照是调和映照和相对仿射映照的条件。 相似文献
3.
Hideki Tsuiki 《Topology and its Applications》2012,159(4):1266-1275
It is shown that every unimodal map is realized as a restriction of a simple map defined on the unit disc to a part of its boundary. Our two-dimensional map is called a full-folding map, which is defined generally on a compact metric space. It is a generalization of the full tent map in that it has two homeomorphic inverse maps and thus every non-critical point has two inverse images. 相似文献
4.
T. D. Narang 《分析论及其应用》2009,25(2):109-116
In 1969, Ky Fan[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x ∈ M such that f (x) - x = dist( f (x), M). Since then, there have appeared several generalizations, extensions and applications of this result. This paper also deals with some extensions and generalizations of this result when the underlying spaces are convex metric spaces. 相似文献
5.
A. V. Ostrovsky 《Proceedings of the American Mathematical Society》2000,128(10):3081-3089
We define the notions of stable and transquotient maps and study the relation between these classes of maps. The class of stable maps contains all closed and open maps and their compositions. The transquotient maps preserve the property of being a Polish space, and every stable map between separable metric spaces is transquotient.
In particular, a composition of closed and open maps (the intermediary spaces may not be metric) preserves the property of being a Polish space. This generalizes the results of Sierpinski and Vainstein for open and closed maps.
6.
7.
Guizhen Cui 《Proceedings of the American Mathematical Society》2001,129(7):1949-1953
We show that two rational maps which are -quasiconformally combinatorially equivalent are -quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy.
8.
数有根近2-正则平面地图 总被引:2,自引:0,他引:2
The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived. 相似文献
9.
A 2-cell embedding f : X → S of a graph X into a closed orientable surface S can be described combinatorially by a pair M = (X;ρ ) called a map, where ρ is a product of disjoint cycle permutations each of which is the permutation of the arc set of X initiated at the same vertex following the orientation of S . It is well known that the automorphism group of M acts semi-regularly on the arc set of X and if the action is regular, then the map M and the embedding f are called regular. Let p and q be primes. Du et al. [J. Algebraic Combin., 19, 123-141 (2004)] classified the regular maps of graphs of order pq . In this paper all pairwise non-isomorphic regular maps of graphs of order 4 p are constructed explicitly and the genera of such regular maps are computed. As a result, there are twelve sporadic and six infinite families of regular maps of graphs of order 4 p ; two of the infinite families are regular maps with the complete bipartite graphs K2p,2p as underlying graphs and the other four infinite families are regular balanced Cayley maps on the groups Z4p , Z22 × Zp and D4p . 相似文献
10.
We study a version of the Gauss map
for a surface
immersed in
and prove an analog of the Ruh--Vilms theorem which states that this map is harmonic iff
has a constant mean curvature. As a corollary, we conclude that an embedded flat torus
with constant mean curvature is a spherical Delonay surface. 相似文献
11.
本文研究了一类Banach空间上凸映射的性质。找出了一类Banach空间上单位球上凸映射的特征,并利用这些结果研究了一类有界凸域上的所有凸映射. 相似文献
12.
Hsu Deliang 《Proceedings of the American Mathematical Society》2005,133(9):2805-2812
In this paper we investigate the regularity of stable-stationary harmonic maps. By assuming that the target manifolds do not carry any stable harmonic , we obtain some compactness results and regularity theorems. In particular, we prove that the Hausdorff dimension of the singular set of these maps cannot exceed , and the dimension estimate is optimal.
13.
关于区间上的Lorenz映射 总被引:1,自引:0,他引:1
本文引进了变换ζ.首先,用比文[4]简捷的方法证明了Lorenz映射的Sarkovski定理并更正了文[4]中的一个错误,还得到了扩张的Lorenz映射中周期点的存在性与其扩张常数之间的关系.其次,证明了Lorenz映射与其在变换ζ的像具有相等的捏制行列式.此外,给出了广义的Lorenz映射的周期点的存在性适合Sarkovski序关系的一个充分条件 相似文献
14.
Yan ZHANG School of Statistics Mathematics Zhejiang Gongshang University Hangzhou China Department of Physics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2007,50(6):859-874
When a target manifold is complete with a bounded curvature, we prove that there exists a unique global solution which satisfies the Euler-lagrange equation of for the given Cauchy data. 相似文献
15.
Charles Ching-An Cheng 《Proceedings of the American Mathematical Society》2001,129(10):2819-2822
In this paper it is proved that a power linear Keller map of dimension three over a field of characteristic zero is linearly triangularizable.
16.
Xian Zu Lin 《数学学报(英文版)》2011,27(5):863-870
Let G/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimensions, for an integer k we can define the Adams map of type k to be l
k
: H*(G/P, ℚ) → H*(G/P, ℚ), l
k
(u) = k
i
u, u ∈ H
2i
(G/P, ℚ). We show that if k is prime to the order of the Weyl group of G, then l
k
can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary. 相似文献
17.
Let S be a smooth minimal projective surface of general type with p_g(S) = q(S) = 1,K_S~2= 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface. 相似文献
18.
19.
We shall prove the equivalences of a non-degenerate circle-preserving map and a Mobius transformation in Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn, of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry. 相似文献
20.
A planar map is a 2-cell embedding of a connected planar graph, loops and parallel edges allowed, on the sphere. A plane map is a planar map with a distinguished outside (“infinite”) face. An unrooted map is an equivalence class of maps under orientation-preserving homeomorphism, and a rooted map is a map with a distinguished oriented edge. Previously we obtained formulae for the number of unrooted planar n-edge maps of various classes, including all maps, non-separable maps, eulerian maps and loopless maps. In this article, using the same technique we obtain closed formulae for counting unrooted plane maps of all these classes and their duals. The corresponding formulae for rooted maps are known to be all sum-free; the formulae that we obtain for unrooted maps contain only a sum over the divisors of n. We count also unrooted two-vertex plane maps. 相似文献