Lightlike real hypersurfaces of indefinite quaternion Kaehler manifold

In this paper, we introduce real lightlike hypersurfaces of indefinite quaternion Kaehler manifold. Fundamental properties of real lightlike hypersurfaces of an indefinite quaternion Kaehler manifold are investigated. We prove the non existence of real lightlike hypersurfaces in indefinite qaternionic space form under some conditions. Received 31 October 2000; revised 20 June 2001.     

Kaehler流形的全脐实超曲面

给出了Ｋａｅｈｌｅｒ流形的全脐实超曲面的一个分类定理。     

Contact Hypersurfaces of a Bochner–Kaehler Manifold

We have studied contact metric hypersurfaces of a Bochner–Kaehler manifold and obtained the following two results: (1) a contact metric constant mean curvature (CMC) hypersurface of a Bochner–Kaehler manifold is a (k, μ)-contact manifold, and (2) if M is a compact contact metric CMC hypersurface of a Bochner–Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V, is isometric to a unit sphere.     

Contact hypersurfaces of Kaehler manifolds

Contact hypersurfaces of a Kaehler manifold have been characterized and classified, assuming the second fundamental form to be Codazzi (in particular, parallel). We have also discussed the special cases when the ambient space is a (i) Calabi-Yau manifold and (ii) a complex space-form.     

Conformal vector fields on Kaehler manifolds

It is known that a conformal vector field on a compact Kaehler manifold is a Killing vector field. In this paper, we are interested in finding conditions under which a conformal vector field on a non-compact Kaehler manifold is Killing. First we prove that a harmonic analytic conformal vector field on a 2n-dimensional Kaehler manifold (n ≠ 2) of constant nonzero scalar curvature is Killing. It is also shown that on a 2n-dimensional Kaehler Einstein manifold (n > 1) an analytic conformal vector field is either Killing or else the Kaehler manifold is Ricci flat. In particular, it follows that on non-flat Kaehler Einstein manifolds of dimension greater than two, analytic conformal vector fields are Killing.     

Hypersurfaces in nearly Kaehler manifold $$\pmb {\mathbb {S}}^{\varvec{3}}\varvec{\times } \pmb {\mathbb {S}}^{\varvec{3}}$$

In this paper, we initiate the study of contact and minimal hypersurfaces in nearly Kaehler manifold \({\mathbb {S}}^3\times {\mathbb {S}}^3\) with a conformal vector field. There are three almost contact metric structures on a hypersurface of \({\mathbb {S}}^3\times {\mathbb {S}}^3\), and we will give some important properties of them. Besides, we study the influence of the conformal vector field on the almost contact metric structures and use it to characterize the hypersurfaces in \({\mathbb {S}}^3\times {\mathbb {S}}^3\).     

Submanifolds of generalized Hopf manifolds,type numbers and the first Chern class of the normal bundle

Summary Any orientable real hypersurface M of a complex Hopf manifold (carrying the locally conformal Kaehler (l.c.K.) metric discovered by I.Vaisman [33]) has a natural f-structure P as a generic Cauchy-Riemann submanifold; we show (cf. our § 5) that if P anti-commutes with the Weingarten operator, then the type number of the hypersurface is less equal than 1. Moreover, M carries the natural almost contact metrical structure observed by Y.Tashiro [30]; if its almost contact vector is an eigenvector of the Weingarten operator corresponding to a nowhere vanishing eigenfunction and the holomorphic distribution is involutive, then M is foliated with globally conformai Kaehler manifolds (cf. our § 5), provided that some restrictions on the type number of M are imposed. We derive (cf. our § 6) a «Simons type» formula and apply it to compact orientable hypersurfaces with non-negative sectional curvature (in a complex Hopf manifold) and parallel mean curvature vector. Several examples of submanifolds of l.c.K. manifolds are exhibited in § 3. Our § 7 studies complex submanifolds of generalized Hopf manifolds; for instance, we show that the first Chern class of the normal bundle of a complex submanifold having a flat normal connection is vanishing.     

Non-existence of Warped Product Semi-Slant Submanifolds of Kaehler Manifolds

In this paper, we show that there are no warped product semi-slant submanifolds of Kaehler manifolds. Contrary to this result,we provide an elementary example of a CR-warped product submanifold of a Kaehler manifold     

Inequalities for cohomology classes of Kaehler manifolds

A set of inequalities for deRham cohomology classes of Kaehler manifolds is proved. As an application, an inequality for Chern numbers of a Kaehler manifold is obtained.     

On submanifolds of Lxf F satisfying Chen's basic equality

It is well known that the warped product Lx_f F of a line L and a Kaehler manifold F is an almost contact Riemannian manifold which is characterized by some tensor equations appeared in (1.7) and (1.8). In this paper we determine submanifolds of Lx_f F which are tangent to the structure vector field and satisfy Chen's basic equality. Also, we investigate tubular hypersurfaces of Lx_f CE ^m which satisfy Chen's basic equality where CE ^m is a complex Euclidean m-space. This revised version was published online in June 2006 with corrections to the Cover Date.     

Geometry of Warped Product CR-Submanifolds in Kaehler Manifolds

 In this paper we study warped product CR-submanifolds in Kaehler manifolds and introduce the notion of CR-warped products. We prove several fundamental properties of CR-warped products in Kaehler manifolds and establish a general inequality for an arbitrary CR-warped product in an arbitrary Kaehler manifold. We then investigate CR-warped products in a general Kaehler manifold which satisfy the equality case of the inequality. Finally we classify CR-warped products in complex Euclidean space which satisfy the equality. (Received 24 August 2000; in revised form 19 February 2001)     

Geometry of formal Kuranishi theory

The principle “ambient cohomology of a Kaehler manifold annihilates obstructions” has been known and exploited since pioneering work of Kodaira. This paper unifies and modestly extends known results in the context of abstract deformations of compact Kaehler manifolds and submanifolds.     

The Type Number of the Cosymplectic Hypersurfaces of 6-Dimensional Hermitian Submanifolds of the Cayley Algebra

We study the 6-dimensional oriented submanifolds of the Cayley algebra which are endowed with the Hermitian structure induced by 3-folds vector cross products. We prove that the type number of a cosymplectic hypersurface of a 6-dimensional Hermitian submanifold of the Cayley algebra is at most 3 and that a 6-dimensional Kaehler submanifold of the octave algebra has no cosymplectic hypersurfaces with the type number greater than one.     

Lightlike Hypersurfaces of a Golden Semi-Riemannian Manifold

We introduce lightlike hypersurfaces of a golden semi-Riemannian manifold. We investigate several properties of lightlike hypersurfaces of a golden semi-Riemannian manifold. We prove that there is no radical anti-invariant lightlike hypersurface of a golden semi-Riemannian manifold. In particular, we obtain some results for screen semi-invariant lightlike hypersurfaces of a golden semi-Riemannian manifold. Moreover, we study screen conformal screen semi-invariant lightlike hypersurfaces.     

Kaehler manifolds satisfying the axiom of anti-invariant 2-spheres

A Kaehler manifold with the axiom of anti-invariant 2-spheres is a complex space form.     

THE MODULI SPACE OF COMPLEX LAGRANGIAN SUBMANIFOLDS IN THE HYPER-KAEHLER MANIFOLD

51.IntroductionSpecialLagrangiansubmanifoldsofaCalabi-Yaumanifoldareoneoftherecentattractivesubjectsinmathematics(see[5-81).In1996,R.C.Mclean[7]obtainedthedeformationtheoremofspeciaILagrangiansubmanifold,whichshowsthat,givenonecompactspecialLagrangiansubmanifoldL,thereisalocalmodulispaceMlwhichisamanifoldandwhosetangelltspaceatLiscanonicallyidentifiedwiththespaceofharmonic1-formsonL.TheLzinnerproductonharmonicformsthengivesthemodulispaceanaturalRiemannianmetric.Strominger,YauandZaslow[1…     

Harmonic Riemannian maps on locally conformal Kaehler manifolds

We study harmonic Riemannian maps on locally conformal Kaehler manifolds (lcK manifolds). We show that if a Riemannian holomorphic map between lcK manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the lcK manifold is Kaehler. Then we find similar results for Riemannian maps between lcK manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.     

On the Spectral Rigidity of Hopf Manifolds

We characterize Hopf manifolds of complex dimension 3 (resp. 2) in the class of compact locally conformal Kaehler manifold ( resp. Hermitian manifold ) by the spectrum of the Laplacian acting on functions.     

局部对称黎曼流形中具有常中曲率完备超曲面

该文研究了局部对称黎曼流形中的具有常平均曲率完备超曲面,获得了超曲面的一个特征定理,此定理推广了一些已有的结论.     

ON FACTORIZATION THEOREMS OF PLURIHARMONIC MAPS INTO THE UNITARY GROUP

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