共查询到20条相似文献,搜索用时 113 毫秒
1.
向量场的Nielsen数 总被引:1,自引:0,他引:1
对于紧致流形M上的任意一个向量场X,定义了一个由向量场X确定的自映射fX:M→M,使得向量场X的奇异点均为fX的不动点.证明了向量场的Nielsen数是不依赖于向量场选取的量. 相似文献
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不动点集为(■P(2r_i+1))■(■S~nj)的对合的流形 总被引:3,自引:1,他引:2
本文讨论了不动点集F为任意多个奇维实数(复数、或者四元数)射影空间与球面不交并的闭流形M上对合T的流形(M,T),给出了这样的流形不协边的充要条件. 相似文献
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混合超图是含有两类超边的超图,一类称为C-超边,一类称为D-超边,它们的区别主要体现在染色要求上.混合超图的染色,要求每一C-超边至少有两个点染相同的颜色,而每一D-超边至少有两个点染不同的颜色.所用的最大颜色数称为对应混合超图的上色数,所用的最小颜色数称为对应混合超图的下色数.上、下色数与边数有密切关系.作者在文献[2]中证明了具有最小上色数的3一致C-超图边数的一个下界为‘n(n-2)/3’,其中n为对应混合超图的顶点数.该文证明当n=2k 1时,该下界是可以达到的. 相似文献
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本文给出了四元数射影空间中紧致全实伪脐子流形关于截面曲率和Ricci曲率的Pinching定理,并推广和改进了四元数射影空间中紧致全实极小流形的一些结果. 相似文献
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本文主要研究了六维近凯勒流形的典范丛和Kodaira维数.证明了六维严格近凯勒流形的典范丛是拟全纯平凡的,从而其Kodaira维数为0.特别地,证明了三维复射影空间CP^3具有Kodaira维数不为-∞的近复结构.对于齐性的六维严格近凯勒流形,具体构造了它们典范丛的整体生成元.证明了齐性近凯勒流形F^3和CP^3的Hodge数h^1,0,h^2,0,h^2,3,h^1,3均为零. 相似文献
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Building on our earlier work on toric residues and reduction, we give a proof of the mixed toric residue conjecture of Batyrev and Materov. We simplify and streamline our technique of tropical degenerations, which allows one to interpolate between two localization principles: one appearing in the intersection theory of toric quotients and the other in the calculus of toric residues. This quickly leads to the proof of the conjecture, which gives a closed formula for the summation of a generating series whose coefficients represent a certain naive count of the numbers of rational curves on toric complete intersection Calabi-Yau manifolds. 相似文献
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This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with two transversal Lagrangian foliations. We also study the non-integrable case (i.e., a symplectic manifold endowed with two transversal Lagrangian distributions). We show that many different geometric structures can be attached to these manifolds and we carefully analyze the associated connections. Moreover, we introduce the problem of the intersection of the two leaves, one of each foliation, through a point and show a lot of significative examples. 相似文献
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Ursula Ludwig 《Comptes Rendus Mathematique》2010,348(15-16):915-918
In this Note we generalise the Witten deformation to even dimensional Riemannian manifolds with cone-like singularities X and certain functions f, which we call admissible Morse functions. As a corollary we get Morse inequalities for the L2-Betti numbers of X. The contribution of a singular point p of X to the Morse inequalities can be expressed in terms of the intersection cohomology of the local Morse datum of f at p. The definition of the class of functions which we study here is inspired by stratified Morse theory as developed by Goresky and MacPherson. However the setting here is different since the spaces considered here are manifolds with cone-like singularities instead of Whitney stratified spaces. 相似文献
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K. Yagasaki 《Journal of Nonlinear Science》1999,9(1):131-148
Summary. We study a two-frequency perturbation of Duffing's equation. When the perturbation is small, this system has a normally hyperbolic
invariant torus which may be subjected to phase locking. Applying a version of Melnikov's method for multifrequency systems,
we detect the occurrence of transverse intersection between the stable and unstable manifolds of the invariant torus. We show
that if the invariant torus is not subjected to phase locking, then such a transverse intersection yields chaotic dynamics.
When the invariant torus is subjected to phase locking, the situation is different. In this case, there exist two periodic
orbits which are created in a saddle-node bifurcation. Using another version of Melnikov's method for slowly varying oscillators,
we also give conditions under which the stable and unstable manifolds of the periodic orbits intersect transversely and hence
chaotic dynamics may occur. Our results reveal that when the invariant torus is subjected to phase locking, chaotic dynamics
resulting from transverse intersection between its stable and unstable manifolds may be interrupted.
Received November 18, 1993; final revision received September 9, 1997; accepted October 27,1997 相似文献
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Jungsoo Kang 《Israel Journal of Mathematics》2012,190(1):111-134
In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. 相似文献
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Jungsoo Kang 《Calculus of Variations and Partial Differential Equations》2013,47(3-4):763-787
Rabinowitz Floer homology has been investigated on submanifolds of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of contact type. In this article, we study Rabinowitz Floer homology for product manifolds which are not necessarily of contact type. We show for a class of product manifolds that there are infinitely many leafwise intersection points by proving the Künneth formula for Rabinowitz Floer homology. 相似文献
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Mohammad A.Asadi-Golmankhaneh 《数学物理学报(B辑英文版)》2011,31(1):259-267
In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the characteristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image ofh : π7QMO(1) → H7QMO(1).In particular, we show that for any immersion of P 6 in R7 the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P 4, 5-fold point manifolds cobordant to P 2 and 7-fold point manifold are odd number. 相似文献
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We consider translators on manifolds with singularities of the type of a transversal intersection of smooth manifolds. We give the definition of ellipticity of translators, prove the finiteness (Fredholm property) theorem, and establish an index formula for the case of point singularities. 相似文献
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Anand Dessai 《Mathematische Nachrichten》1998,192(1):159-172
In the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10-manifold M with H1(M;?) = 0 and no 2-torsion in H1(M;?) for i = 2,3. Using the Classification Theorem of Donaldson we give a reformulation of the conditions for a 4-manifold to be almost complex in terms of Betti numbers and the dimension of the ±-eigenspaces of the intersection form. In the second part we give general conditions for an almost complex manifold to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete intersections. 相似文献
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Cenap Özel 《Topology and its Applications》2006,153(12):2104-2117
In [A.J. Baker, C. Ozel, Complex cobordism of Hilbert manifolds with some applications to flag varieties, Contemp. Math. 258 (2000) 1-19], by using Fredholm index we developed a version of Quillen's geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In [C. Ozel, On Fredholm index, transversal approximations and Quillen's geometric complex cobordism of Hilbert manifolds with some applications to flag varieties of loop groups, in preparation], by using Quinn's Transversality Theorem [F. Quinn, Transversal approximation on Banach manifolds, Proc. Sympos. Pure Math. 15 (1970) 213-222], it has been shown that this cobordism theory has a graded ring structure under transversal intersection operation and has pull-back maps for smooth maps. It has been shown that the Thom isomorphism in this theory was satisfied for finite dimensional vector bundles over separable Hilbert manifolds and the projection formula for Gysin maps has been proved. In [M. Chas, D. Sullivan, String topology, math.GT/9911159, 1999], Chas and Sullivan described an intersection product on the homology of loop space LM. In [R.L. Cohen, J.D.S. Jones, A homotopy theoretic realization of string topology, math.GT/0107187, 2001], R. Cohen and J. Jones described a realization of the Chas-Sullivan loop product in terms of a ring spectrum structure on the Thom spectrum of a certain virtual bundle over the loop space. In this paper, we will extend this product on cobordism and bordism theories. 相似文献