共查询到20条相似文献,搜索用时 15 毫秒
1.
Bang-Yen Chen 《Monatshefte für Mathematik》2001,134(2):103-119
A CR-submanifold N of a Kaehler manifold is called a CR-warped product if N is the warped product of a holomorphic submanifold and a totally real submanifold of . This notion of CR-warped products was introduced in part I of this series. It was proved in part I that every CR-warped product in a Kaehler manifold satisfies a basic inequality: . The classification of CR-warped products in complex Euclidean space satisfying the equality case of the inequality is archived in part I. The main
purpose of this second part of this series is to classify CR-warped products in complex projective and complex hyperbolic spaces which satisfy the equality.
(Received 13 March 2001; in revised form 10 August 2001) 相似文献
2.
Bang-Yen Chen 《Monatshefte für Mathematik》2004,141(3):177-186
A submanifold of a Kaehler manifold is called a CR-warped product if it is the warped product NT ×fN of a complex submanifold NT and a totally real submanifold N. There exist many CR-warped products NT ×fN in CPh+p, h = dimCNT and p = dimRN (see [5, 6]). In contrast, we prove in this article that the situation is quite different if the holomorphic factor NT is compact. For such CR-wraped products in CPm (4), we prove the following: (1) The complex dimension m of the ambient space is at least h + p + hp. (2) If m = h + p + hp, then NT is CPh(4). We also obtain two geometric inequalities for CR-warped products in CPm with compact NT. 相似文献
3.
Bang-Yen Chen 《Monatshefte für Mathematik》2001,109(1):103-119
A CR-submanifold N of a Kaehler manifold is called a CR-warped product if N is the warped product of a holomorphic submanifold and a totally real submanifold of . This notion of CR-warped products was introduced in part I of this series. It was proved in part I that every CR-warped product in a Kaehler manifold satisfies a basic inequality: . The classification of CR-warped products in complex Euclidean space satisfying the equality case of the inequality is archived in part I. The main purpose of this second part of this series is to classify CR-warped products in complex projective and complex hyperbolic spaces which satisfy the equality. 相似文献
4.
Bang-Yen Chen 《Monatshefte für Mathematik》2007,151(2):143-152
Let π : M → B be a Riemannian submersion with minimal fibers. In this article we prove the following results: (1) If M is positively curved, then the horizontal distribution of the submersion is a non-totally geodesic distribution; (2) if M is non-negatively (respectively, negatively) curved, then the fibers of the submersion have non-positive (respectively, negative)
scalar curvature; and (3) if M can be realized either as an elliptic proper centroaffine hypersphere or as an improper hypersphere in some affine space,
then the horizontal distribution is non-totally geodesic. Several applications are also presented. 相似文献
5.
Paola Matzeu 《Monatshefte für Mathematik》2002,136(4):297-311
We consider compact Weyl submanifolds of Weyl flat manifolds with special attention on compact Einstein-Weyl hypersurfaces.
In particular, in the last part of the paper, we study Weyl submanifolds of special noncompact manifolds, called PC-manifolds.
Received July 16, 2001; in revised form February 6, 2002 Published online August 9, 2002 相似文献
6.
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
7.
Our main theorem is a characterization of a totally geodesic K?hler immersion of a complex n-dimensional K?hler manifold M
n
into an arbitrary complex (n + p)-dimensional K?hler manifold
by observing the extrinsic shape of K?hler Frenet curves on the submanifold M
n
. Those curves are closely related to the complex structure of M
n
. 相似文献
8.
Changyu Xia 《Monatshefte für Mathematik》2005,146(2):159-168
Let Sn(c) denote the n-dimensional Euclidean sphere of constant sectional curvature c and denote by CPn(c) the complex projective space of complex dimension n and of holomorphic sectional curvature c. In this paper, we obtain some characterizations of the manifolds S2(c) × S2(c′), S4(c) × S4(c′), CP2(c) × CP2(c′) by their spectrum. 相似文献
9.
Given a submanifold M
n
of Euclidean space ℝ
n
+
p
with codimension p≤6, under generic conditions on its second fundamental form, we show that any other isometric immersion of M
n
into ℝ
n
+
p
+
q
, 0≤q≤n− 2p−1 and 2q≤n+ 1 if q≥ 5, must be locally a composition of isometric immersions. This generalizes several previous results on rigidity and compositions
of submanifolds. We also provide conditions under which our result is global.
14 March 2001 相似文献
10.
Guoxin Wei 《Monatshefte für Mathematik》2006,149(4):343-350
By investigating hypersurfaces M
n
in the unit sphere S
n+1(1) with H
k
= 0 and with two distinct principal curvatures, we give a characterization of torus the
. We extend recent results of Perdomo [9], Wang [10] and Otsuki [8]. 相似文献
11.
Guoxin Wei 《Monatshefte für Mathematik》2006,149(3):251-258
By investigating hypersurfaces M
n
in the unit sphere S
n+1(1) with constant mean curvature and with two distinct principal curvatures, we give a characterization of the torus S
1(a) ×
, where
. We extend recent results of Hasanis et al. [5] and Otsuki [10]. 相似文献
12.
In this paper, we will introduce the notion of harmonic stability for complete minimal hypersurfaces in a complete Riemannian
manifold. The first result we prove, is that a complete harmonic stable minimal surface in a Riemannian manifold with non-negative
Ricci curvature is conformally equivalent to either a plane R
2 or a cylinder R × S
1, which generalizes a theorem due to Fischer-Colbrie and Schoen [12].
The second one is that an n ≥ 2-dimensional, complete harmonic stable minimal, hypersurface M in a complete Riemannian manifold with non-negative sectional curvature has only one end if M is non-parabolic. The third one, which we prove, is that there exist no non-trivial L
2-harmonic one forms on a complete harmonic stable minimal hypersurface in a complete Riemannian manifold with non-negative
sectional curvature. Since the harmonic stability is weaker than stability, we obtain a generalization of a theorem due to
Miyaoka [20] and Palmer [21].
Research partially Supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science
and Technology, Japan.
The author’s research was supported by grant Proj. No. KRF-2007-313-C00058 from Korea Research Foundation, Korea.
Authors’ addresses: Qing-Ming Cheng, Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga
840-8502, Japan; Young Jin Suh, Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea 相似文献
13.
Franki Dillen Johan Fastenakels Joeri Van der Veken Luc Vrancken 《Monatshefte für Mathematik》2007,152(2):89-96
In this article we study surfaces in
for which the unit normal makes a constant angle with the
-direction. We give a complete classification for surfaces satisfying this simple geometric condition. 相似文献
14.
In this paper we construct many ruled real hypersurfaces in a nonflat quaternionic space form systematically, and in particular give an example of a homogeneous ruled real hypersurface in a quaternionic hyperbolic space. In the second half of this paper we characterize them by investigating the extrinsic shape of their geodesics. We also characterize curvature-adapted real hypersurfaces in nonflat quaternionic space forms from the same viewpoint.The first author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 14540075), Ministry of Education, Science, Sports and Culture.The second author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 14540080), Ministry of Education, Science, Sports and Culture. 相似文献
15.
We construct new examples of embedded, complete, minimal hypersurfaces in complex hyperbolic space, including deformations of bisectors and some minimal foliations. Received: 20 March 2000 / Revised version: 21 July 2000 相似文献
16.
Qiaoling Wang 《Monatshefte für Mathematik》2003,140(2):163-167
In this paper, we prove some rigidity theorems for Clifford minimal hypersurfaces in a unit sphere.Received March 18, 2002; in revised form December 25, 2002
Published online October 15, 2003 相似文献
17.
Toshiaki Adachi 《Monatshefte für Mathematik》2008,153(4):283-293
In this paper, we study geodesics with null structure torsions on real hypersurfaces of type A
2 in a complex space form. These geodesics give a nice family of helices of order 3 generated by Killing vector fields on the
ambient complex space form.
Author’s address: Toshiaki Adachi, Department of Mathematics, Nagoya Institute of Technology, Nagoya 466-8555, Japan 相似文献
18.
In the Riemannian case, our approach to warped products illuminates curvature formulas that previously seemed formal and somewhat
mysterious. Moreover, the geometric approach allows us to study warped products in a much more general class of spaces. For
complete metric spaces, it is known that nonpositive curvature in the Alexandrov sense is preserved by gluing on isometric
closed convex subsets and by Gromov–Hausdorff limits with strictly positive convexity radius; we show it is also preserved
by warped products with convex warping functions.
Received: 9 January 1998/ Revised version: 12 March 1998 相似文献
19.
In this paper, we are interested in extending the study of spherical curves in R
3 to the submanifolds in the Euclidean space R
n+p
. More precisely, we are interested in obtaining conditions under which an n-dimensional compact submanifold M of a Euclidean space R
n+p
lies on the hypersphere S
n+p−1(c) (standardly imbedded sphere in R
n+p
of constant curvature c). As a by-product we also get an estimate on the first nonzero eigenvalue of the Laplacian operator Δ of the submanifold
(cf. Theorem 3.5) as well as a characterization for an n-dimensional sphere S
n
(c) (cf. Theorem 4.1). 相似文献
20.
S. Haesen 《Monatshefte für Mathematik》2007,152(4):303-314
Surfaces with positive definite second fundamental form in a Riemannian, three-dimensional warped product space are considered.
A formula expressing the Gaussian curvature with respect to this new metric on the surface in terms of the Gaussian and mean
curvature of the first fundamental form is presented. This formula is then used to give some characterizations of compact,
totally umbilical surfaces.
Postdoctoral researcher of the F.W.O. Vlaanderen. 相似文献