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1.
Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [9]). The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen's work on CR-warped product submanifolds of Kaehler manifolds (cf. [6], [7]). Later on, similar studies were carried out in the setting of 1.c.K. manifolds and nearly Kaehler manifolds (el. [3], [11]). In the present article, we investigate a larger class of warped product submanifolds of 1.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold. 相似文献
2.
Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [9]). The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen's work on CR-warped product submanifolds of Kaehler manifolds (cf. [6], [7]). Later on, similar studies were carried out in the setting of l.c.K. manifolds and nearly Kaehler manifolds (cf. [3], [11]). In the present article, we investigate a larger class of warped product submanifolds of l.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold. 相似文献
3.
Bayram Sahin 《Geometriae Dedicata》2006,117(1):195-202
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 相似文献
4.
In this paper, we study pseudo-slant submanifolds and their warped products in Kenmotsu manifolds. We obtain the necessary conditions that a pseudoslant submanifold is locally a warped product and establish an inequality for the squared norm of the second fundamental form in terms of the warping function. The equality case is also considered. 相似文献
5.
Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. The equality case is considered. Also, the minimum codimension of a contact CR-warped product in an odd-dimensional sphere is determined. 相似文献
6.
A submanifold M of an almost Hermitian manifold \((\widetilde{M},g,J)\) is called slant, if for each point \(p\in M\) and \(0\ne X\in T_p M\), the angle between JX and \(T_p M\) is constant (see Chen in Bull Aust Math Soc 41:135–147, 1990). Later, Carriazo (in: Proceedings of the ICRAMS 2000, Kharagpur, 2000) defined the notion of bi-slant immersions as an extension of slant immersions. In this paper, we study warped product bi-slant submanifolds in Kaehler manifolds and provide some examples of warped product bi-slant submanifolds in some complex Euclidean spaces. Our main theorem states that every warped product bi-slant submanifold in a Kaehler manifold is either a Riemannian product or a warped product hemi-slant submanifold. 相似文献
7.
M. -I. Munteanu 《Acta Mathematica Hungarica》2007,116(1-2):121-126
Warped product C R-submanifolds in Kählerian manifolds were intensively studied only since 2001 after the impulse given by B. Y. Chen in [3], [4]. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kählerian geometry, was developed, namely warped product contact C R-submanifolds in Sasakian manifolds (cf. [7], [8]). In this note we prove that there exists no proper doubly warped product contact C R-submanifolds in trans-Sasakian manifolds. 相似文献
8.
Marian Ioan Munteanu 《Monatshefte für Mathematik》2007,117(1):333-342
In this paper we study doubly warped product CR submanifolds in locally conformal K?hler manifolds, and we found a B.Y. Chen’s type inequality for the second fundamental
form of these submanifolds. 相似文献
9.
The main objective of this paper is to study the warped product pointwise semi‐slant submanifolds which are isometrically immersed into Sasakian manifolds. First, we prove some characterizations results in terms of the shape operator, under which influence a pointwise semi‐slant submanifold of a Sasakian manifold can be reduced to a warped product submanifold. Then, we determine a geometric inequality for the second fundamental form regarding to intrinsic invariant and extrinsic invariant using the Gauss equation instead of the Codazzi equation. Evenmore, we give some applications of this inequality into Sasakian space forms, and we will investigate the status of equalities in the inequality. As a particular case, we provide numerous applications of the Green lemma, the Laplacian of warped functions and some partial differential equations. Some triviality results for connected, compact warped product pointwise semi‐slant submanifolds of Sasakian space form by means of Hamiltonian and the kinetic energy of warped function involving boundary conditions are established. 相似文献
10.
We prove that a nearly Kenmotsu manifold is locally isometric to the warped product of a real line and a nearly Kähler manifold. As consequence, a normal nearly Kenmotsu manifold is Kenmotsu. Furthermore, we show that there do not exist nearly Kenmotsu hypersurfaces of nearly Kähler manifolds.
相似文献11.
Marian Ioan Munteanu 《Monatshefte für Mathematik》2007,150(4):333-342
In this paper we study doubly warped product CR submanifolds in locally conformal K?hler manifolds, and we found a B.Y. Chen’s type inequality for the second fundamental
form of these submanifolds.
Beneficiary of a CNR-NATO Advanced Research Fellowship pos. 216.2167 Prot. n. 0015506. 相似文献
12.
We give a procedure to ‘average’ canonically C1-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves
a Legendrian submanifold almost invariant, there is an invariant Legendrian submanifold nearby.
Mathematics Subject Classification (2000): 53D10. 相似文献
13.
Bang-Yen Chen 《Annali di Matematica Pura ed Applicata》2006,185(4):555-576
The notion of contact number
of a Euclidean submanifold was introduced in an earlier article (Proc. Edinb. Math. Soc. 47:69–100, 2004) as the highest
order of contact of geodesics and normal sections on the submanifold. It was proved in (Proc. Edinb. Math. Soc. 47:69–100,
2004) that the contact number relates closely with the notions of isotropic submanifolds and holomorphic curves. One important
problem concerning contact number is to construct Euclidean submanifolds with high contact number. The purpose of this article
is thus to construct Euclidean surfaces with high contact number and to provide simple geometric characterization of such
surfaces.
Mathematics Subject Classification (2000) Primary 53C40, 53A10 Secondary 53B25, 53C42 相似文献
14.
Qiaoling Wang Changyu Xia 《Calculus of Variations and Partial Differential Equations》2011,40(1-2):273-289
In this paper we study eigenvalues of a clamped plate problem on compact domains in complete manifolds. For complete manifolds admitting special functions, we prove universal inequalities for eigenvalues of clamped plate problem independent of the domains of Payne?CPólya?CWeinberger?CYang type. These manifolds include Hadamard manifolds with Ricci curvature bounded below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifolds and manifolds admitting eigenmaps to a sphere. In the case of warped product manifolds, our result implies a universal inequality on hyperbolic space proved by Cheng?CYang. We also strengthen an inequality for eigenvalues of clamped plate problem on submanifolds in a Euclidean space obtained recently by Cheng, Ichikawa and Mametsuka. 相似文献
15.
Demir N. Kupeli 《Geometriae Dedicata》1987,24(3):337-361
Degenerate submanifolds of Semi-Riemannian manifolds are studied. The relation of the Semi-Riemannian structure of a Semi-Riemannian manifold M to the intrinsic singular Semi-Riemannian structure of a degenerate submanifold H in M is investigated. Gauss-Codazzi equations are obtained for a certain class of degenerate submanifolds of Semi-Riemannian manifolds. 相似文献
16.
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. 相似文献
17.
The purpose of this paper is to study the pointwise pseudo-slant warped product submanifolds of a Kähler manifold \(\widetilde{M}\). We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a pointwise pseudo-slant submanifolds of \(\widetilde{M}\). The necessary and sufficient conditions for isometrically immersed pointwise pseudo-slant submanifolds of \(\widetilde{M}\) to be a pointwise pseudo-slant warped product and a locally Riemannian product are obtained. Further, we classify pointwise pseudo-slant warped product submanifolds of \(\widetilde{M}\) by developing the sharp inequalities in terms of second fundamental form and wrapping function. 相似文献
18.
In this paper, we establish a sharp inequality for the squared norm of the second fundamental form of bi-warped product submanifolds of Kenmotsu manifolds. The equality case is also considered. We also provide a non-trivial example and some applications of derived inequality. 相似文献
19.
Periodica Mathematica Hungarica - We introduce sequential warped product submanifolds of Kaehler manifolds, provide examples and establish Chen’s inequality for such submanifolds. The... 相似文献
20.
Manfredo P. do Carmo Qiaoling Wang Changyu Xia 《Annali di Matematica Pura ed Applicata》2010,189(4):643-660
In this paper, we study eigenvalues of elliptic operators in divergence form on compact Riemannian manifolds with boundary
(possibly empty) and obtain a general inequality for them. By using this inequality, we prove universal inequalities for eigenvalues
of elliptic operators in divergence form on compact domains of complete submanifolds in a Euclidean space, and of complete
manifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below, a class of
warped product manifolds, the product of Euclidean spaces with any complete manifold and manifolds admitting eigenmaps to
a sphere. 相似文献