核心的余维数为1的具非负曲率完备非紧黎曼流形

利用G .Perelman证明“核心猜想”的思想证明了对n维完备非紧具非负曲率的黎曼流形 ,若其核心之维数是n - 1,则该流形可等距分裂为S×R .其中S为该流形的核心 .     

具非负Ricci曲率和严格（1＋δ）阶体积增长的三维流形

本文研究了三维完备非紧具非负Ricci曲率的黎曼流形的几何拓扑性质.通过对流形本身与流形的万有覆盖空间体积增长阶的比较,证明了对具非负Ricci曲率和严格(1+δ)阶体积增长的三维完备非紧的黎曼流形是可缩的.     

具非负曲率完备非紧曲面的几何性质

本文证明了单连通完备非紧具非负曲率之曲面的任一测地线γ：[0,+∞)→M均趋于∞处这一几何性质,指出了一般的高维流形不具有此性质.本文还证明了单连通完备非紧具非负曲率的曲面的割迹与第一共轭轭迹是一致的;并且讨论了一般高维流形的共轭点与测地线的关系.     

完备非紧具非负曲率流形之拓扑结构

本文给出完备非紧具非负曲率的Riemann流形具有限拓扑型的一个简单证明.     

具非负Ricci曲率和强有界几何条件的流形

设M是具非负Ricci曲率的n维完备非紧黎曼流形,若M具次大体积增长vol{B(p,r)1≥βM*, p ∈M, r≥1和满足强有界几何条件,则M具有限拓扑型.     

完备非紧具非负曲率流形之拓扑结构

本文给出完备非紧具非负曲率的Ｒｉｅｍａｎｎ流形具有限拓扑型的一个简单证明     

完备Riemann流形之共轭点

本文证明了具非负曲率完备Ｒｉｅｍａｎｎ测地线为无共轭点测地线的充要条件；并由此证明了若该流形上的截面含有一无共轭点测地线的切向量，则其对应的截曲率为零．     

完备Riemann流形中的测地子流形的焦点

利用沿测地线的N-Jacobi场和指标形式,得到了具非负曲率完备Riemann流形中的测地子流形为无焦点的充要条件。     

关于H. Wu问题

著名几何学家Ｈ．Ｗｕ在「４」中提出这样的问题：若一完备非紧的黎曼流形仅有两个符号相反的Ｂｕｓｅｍａｎｎ函数,则该流形的结构如何？本文在流形具非负Ｒｉｃｃｉ曲率或截曲率具下界的情况下部分地解决了这一问题。同时还讨论了流形在具非负曲率条件下有关的一些性质。     

径向截面曲率有下界黎曼流形的微分同胚定理

研究了径向截面曲率以一类旋转模曲面的Gauss曲率为下界的非紧完备黎曼流形的拓扑,得到了该类黎曼流形与欧氏空间微分同胚的一个合理的充分条件,推广了径向截面曲率有常数下界完备黎曼流形的微分同胚定理.     

Equivariant Chern Classes of Orientable Toric Origami Manifolds∗

A toric origami manifold, introduced by Cannas da Silva, Guillemin and Pires, is a generalization of a toric symplectic manifold. For a toric symplectic manifold, its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line bundles. But in general a toric origami manifold is not simply connected, so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic manifold. In this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami template. Furthermore, they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.     

A Note on P—Sasakian Manifold

s51.IntroductionLetMbeadifferentiablemanifo1dofdimensionn,ifMadmitsa(l,l)-tensorfieldgl,aPoSitivedefiniteRiemannianmetricg,avectorfieldeandal-formVwhichsatisfythefollow-ingconditions.thensuchamanifoldMiscalledaPara-SasakianmanifoldorbrieflyaP-Sasakianmanifoldby7'.AdatiandK.Matsumoto[ljwhichareconsideredasspecialcaseofanalmostparacontactmanifoldintroducedbyI.Sato[2].WhereVdenotestheoperatorofcovariantdifferentiationwithrespecttothemetrictensorg'X(M)denotesthesetofdifferentiablevectorfiel…     

非线性发展方程的H(o)lder连续惯性流形

引入非线性发展方程的H\"older连续惯性流形的概念,为原来惯性流形概念的推广和修正.惯性流形是有限维不变的Lipschiz流形,是研究发展方程解的长时间性态的合适工具,其缺点是需要谱间隙条件.提出H\"older连续惯性流形也是有限维不变的,但光滑性减弱为H\"older连续,不需要谱间隙条件.该流形与指数吸引子交集具有指数吸引性,无穷维动力系统可在H\"older连续惯性流形上约化为有限维常微分方程组.     

On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems

We consider a family of boundary-value problems with some potential as a parameter. We study the manifold of normalized eigenfunctions with even number of zeros in a period, and the manifold of potentials associated with double eigenvalues. In particular, we prove that the manifold of normalized eigenfunctions is a trivial fiber space over a unit circle and that the manifold of potentials with double eigenvalues is a homotopically trivial manifold trivially imbedded into the space of potentials.     

A manifold that does not contain a compact core

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.     

A curvature condition for a twisted product¶to be a warped product

It is shown that a mixed Ricci-flat twisted product semi-Riemannian manifold can be expressed as a warped product semi-Riemannian manifold. As a consequence, any Einstein twisted product semi-Riemannian manifold is in fact, a warped product semi-Riemannian manifold. Received: 8 March 2001 / Revised version: 25 July 2001     

Some constraints on Frobenius manifolds with a tt*-structure

The article gives a necessary and sufficient condition for a Frobenius manifold to be a CDV-structure. We show that there exists a positive definite CDV-structure on any semi-simple Frobenius manifold. We also compare three natural connections on a CDV-structure and conclude that the underlying Hermitian manifold of a non-trivial CDV-structure is not a K?hler manifold. Finally, we compute the harmonic potential of a harmonic Frobenius manifold.     

On doubly warped product Finsler manifolds

In this paper, we introduce horizontal and vertical warped product Finsler manifolds. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemannian curvatures of doubly warped product Finsler manifold and its components, and consider the cases that this manifold is flat or has scalar flag curvature. We define the doubly warped Sasaki-Matsumoto metric for warped product manifolds and find a condition under which the horizontal and vertical tangent bundles are totally geodesic. We obtain some conditions under which a foliated manifold reduces to a Reinhart manifold. Finally, we study an almost complex structure on the tangent bundle of a doubly warped product Finsler manifold.     

On a Submersion Between Reinhart Lightlike Manifolds and Semi-Riemannian Manifolds

In this paper, we introduce a new submersion, namely, screen lightlike submersion between a lightlike manifold and a semi-Riemannian manifold. We give an example and obtain a characterization for lightlike manifold to be Reinhart under such submersion. Then, we investigate the geometry of a screen lightlike submersion when the total manifold is a Reinhart lightlike manifold. Received: March 6, 2007 Revised: October 4, 2007 and November 2, 2007 Accepted: December 6, 2007