Stein fillability and the realization of contact manifolds

There is an intrinsic notion of what it means for a contact manifold to be the smooth boundary of a Stein manifold. The same concept has another more extrinsic formulation, which is often used as a convenient working hypothesis. We give a simple proof that the two are equivalent. Moreover it is shown that, even though a border always exists, its germ is not unique; nevertheless the germ of the Dolbeault cohomology of any border is unique. We also point out that any Stein fillable compact contact -manifold has a geometric realization in via an embedding, or in via an immersion.

     

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…     

On Flat Complete Causal Lorentzian Manifolds

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental groups are virtually abelian. In dimension 4, there is only one, up to a scaling factor, strictly causal manifold which is not globally hyperbolic. For a generic point of this manifold, either the past or the future is not closed and contains a lightlike straight line     

Some remarks about 1-convex manifolds on which all holomorphic line bundles are trivial

We give an abridged proof of an example already considered in [M. Col?oiu, On 1-convex manifolds with 1-dimensional exceptional set, Rev. Roumaine Math. Pures et Appl. 43 (1998) 97-104] of a 1-convex manifold X of dimension 3 such that all holomorphic line bundles on X are trivial. We also point out several mistakes of [Vo Van Tan, On the quasiprojectivity of compactifiable strongly pseudoconvex manifolds, Bull. Sci. Math. 129 (2005) 501-522] concerning this topic.     

ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES I

In this paper the authors investigate hypersurfaces M of a semi-Euclidean space Esn+1, n > 4, satisfying (aC + BR) ?H = LkQ(g, Hk), k = 1,2, 3. Using obtained results they show additional curvature properties of investigated hypersurfaces.     

ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES Ⅰ

In this paper the authors investigate hypersurfaces M of a semi-Euclidean space Esn+1, n ≥ 4, satisfying (aC +βR). H ＝ LkQ(g, Hk), k ＝ 1,2,3. Using obtained results they show additional curvature properties of investigated hypersurfaces.     

Contactly geodesic transformations of almost-contact metric structures

We introduce the notion of contactly geodesic transformation of the metric of an almost-contact metric structure as a contact analog of holomorphically geodesic transformations of the metric of an almost-Hermitian structure. A series of invariants of such transformations is obtained. We prove that such transformations preserve the normality property of an almost-contact metric structure. We prove that cosymplectic and Sasakian manifolds, as well as Kenmotsu manifolds, do not admit nontrivial contactly geodesic transformations of the metric, which is a contact analog of the well-known result for Kählerian manifolds due to Westlake and Yano.     

The signature of generalized flag manifolds and applications

Let G be a linear algebraic group over C and P be a parabolic subgroup. We determine the signatures of the flag manifold G/P. As an application, we prove that the nonsingular hypersurfaces of degree 2 in CP^n are prime if n satisfies certain conditions.     

Invariant manifolds for a singular ordinary differential equation

We study the singular ordinary differential equation

(0.1)     

ISOTROPIC WEYL MANIFOLD WITH A SEMI-SYMMETRIC CONNECTION

In this work,it is proved that every isotropic Weyl manifold with a semi- symmetric connection is locally conformal to an Einstein manifold with a semi-symmetric connection.     

Theorems of Barth–Lefschetz type in Sasakian geometry

In this paper, we obtain theorems of Barth–Lefschetz type in Sasakian geometry. As a corollary, this gives a new proof of a classical theorem due to J. Milnor. It also implies connectedness principle and Frankel's type theorem.     

Sasakian structures on CR-manifolds

A contact manifold M can be defined as a quotient of a symplectic manifold X by a proper, free action of \(\mathbb{R}\), with the symplectic form homogeneous of degree 2. If X is also Kähler, and its metric is homogeneous of degree 2, M is called Sasakian. A Sasakian manifold is realized naturally as a level set of a Kähler potential on a complex manifold, hence it is equipped with a pseudoconvex CR-structure. We show that any Sasakian manifold M is CR-diffeomorphic to an S ¹-bundle of unit vectors in a positive line bundle on a projective Kähler orbifold. This induces an embedding of M into an algebraic cone C. We show that this embedding is uniquely defined by the CR-structure. Additionally, we classify the Sasakian metrics on an odd-dimensional sphere equipped with a standard CR-structure.     

股票市场模型和不变价格流形

本文首次提出股票市场价格流形的概念 ,并对由维纳过程 (布朗运动 )驱动的市场价格动态扩散过程模型 (X)的不变流形作了初步的讨论 ,给出了一个判定一个给定的价格流形M是市场模型 (X)的不变流形的充分条件 .     

On geometry of flat complete strictly causal Lorentzian manifolds

A flat complete causal Lorentzian manifold is called strictly causal if the past and future of its every point are closed near this point. We consider the strictly causal manifolds with unipotent holonomy groups and assign to a manifold of this type four nonnegative integers (a signature) and a parabola in the cone of positive definite matrices. Two manifolds are equivalent if and only if their signatures coincide and the corresponding parabolas are equal (up to a suitable automorphism of the cone and an affine change of variable). Also, we give necessary and sufficient conditions distinguishing the parabolas of this type among all parabolas in the cone.     

V-流形间的2-调和映照

本文将２－调和映照从黎曼流形推广到Ｖ－流形,获得了２－调和映照的第一变分和第二变分,得到了２－调和映照成为调和映照的一些充分条件,讨论了Ｖ－流形上２－调和映照的复合映照。     

Einstein Metrics,Symplectic Minimality,and Pseudo-Holomorphic Curves

An alternative proof of the uniformization theorem for compact two-dimensional riemannian surfaces of genus 0 is proved via the direct methods of the calculus of variation as a minimum problem of the metric-dependent Dirichlet energy in the class of those maps with degree 1. Because of the conformal invariance of the energy-functional and the non compactness of the conformal group on S², concentration of mass for sequences can occur and spheres can split off. Nevertheless this is not the case for appropriate conformaly retransformed minimizing sequences. The main argument is the verification of a condition of the Douglas-type.     

关于带有Ricci孤子的trans-Sasakian流形的注记(英文)

本文主要研究带有Ricci孤子的(α,β)型trans-Sasakian流形,证明了带有Ricci孤子(g,ξ,λ)的3-维紧致trans-Sasakian流形是一个Sasakian流形.此外,如果α,β是常数,得到带有梯度Ricci孤子的trans-Sasakian流形是Einstein流形.