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21.
HAN Mao''''an & CHEN Xianfeng Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Shanghai Jiao Tong University Shanghai China 《中国科学A辑(英文版)》2005,48(7):940-957
In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved. 相似文献
22.
A characterization of the Ejiri torus in <Emphasis Type="Italic">S</Emphasis><Superscript>5</Superscript> 下载免费PDF全文
Peng Wang 《数学学报(英文版)》2016,32(9):1014-1026
We conjecture that a Willmore torus having Willmore functional between 2π 2 and 2π 2 \(\sqrt 3 \) is either conformally equivalent to the Clifford torus, or conformally equivalent to the Ejiri torus. Ejiri’s torus in S 5 is the first example of Willmore surface which is not conformally equivalent to any minimal surface in any real space form. Li and Vrancken classified all Willmore surfaces of tensor product in S n by reducing them into elastic curves in S 3, and the Ejiri torus appeared as a special example. In this paper, we first prove that among all Willmore tori of tensor product, the Willmore functional of the Ejiri torus in S 5 attains the minimum 2π 2 \(\sqrt 3 \), which indicates our conjecture holds true for Willmore surfaces of tensor product. Then we show that all Willmore tori of tensor product are unstable when the co-dimension is big enough. We also show that the Ejiri torus is unstable even in S 5. Moreover, similar to Li and Vrancken, we classify all constrained Willmore surfaces of tensor product by reducing them with elastic curves in S 3. All constrained Willmore tori obtained this way are also shown to be unstable when the co-dimension is big enough. 相似文献
23.
24.
Bruce Solomon 《Geometriae Dedicata》2007,128(1):33-37
We produce skew loops—loops having no pair of parallel tangent lines—homotopic to any loop in a flat torus or other quotient of R
n
. The interesting case here is n = 3. More subtly for any n, we characterize the homotopy classes that will contain a skew loop having a specified loop as tangent indicatrix.
A fellowship from the Lady Davis foundation helped support this work. 相似文献
25.
R. A. Vikent’ev 《Siberian Mathematical Journal》2007,48(3):428-429
In the automorphism group of a rank 3 free group we find two nonconjugate automorphisms whose mapping tori are isomorphic groups. 相似文献
26.
一类量子环面李代数的自同构群 总被引:3,自引:0,他引:3
=C_q[x_1~(±1),x_2~(±1)]为复数域上的非交换环面结合代数,A=\C,Der为的导子李代数.本文研究李代数L_q=DerA的自同构群Aut L_q. 相似文献
27.
I. Mundet i Riera 《Advances in Mathematics》2007,214(1):469-493
Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x,y)∈X×X|y=gx for some g∈G} defines a nonzero equivariant cohomology class . We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a Hamiltonian action of a torus, whose complexification plays the role of G. We also prove that the Kirwan map sends the class [ΔG] to the class of the diagonal in each symplectic quotient. This allows to define a canonical right inverse of the Kirwan map. 相似文献
28.
M. A. Ovchinnikov 《Mathematical Notes》1999,66(4):436-441
In 1991, Turaev and Viro constructed a quantum topological linear representation of mapping class groups of closed surfaces.
To the mappings of a surface into itself, they assigned simple polyhedra whose boundaries consisted of two simple graphs cutting
the surface into cells. The computational complexity of the Turaev-Viro representations strongly depends on the choice of
suitable sets of simple polyhedra. In this paper, simple polyhedra for the torus are constructed. One of the reasons why they
are convenient is that they all are obtained by gluing along boundary of copies of the same simple polyhedron.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 533–539, October, 1999. 相似文献
29.
研究具有循环调和序列的平坦极小浸入ψ:T2→CPn。证明了存在T2的一个有限覆盖p:T2→T2和一个全迷向的平坦极小浸入φ:T2→CPn使得ψ。p=A。φ,其中A:CPn→CPn:[v]→[vA]是线性全纯同胚。 相似文献
30.
Eon-Kyung Lee 《代数通讯》2013,41(3):1121-1139
In this article, we show that for every abelian subgroup H of a Garside group, some conjugate g ?1 Hg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups. 相似文献