共查询到20条相似文献,搜索用时 15 毫秒
1.
We characterize some homogeneous Hopf real hypersurfaces in a nonflat complex space form by studying trajectories for Sasakian magnetic fields whose extrinsic shapes are tangentially of order 2. 相似文献
2.
The purpose of this paper is to define a ruled real hypersurface of a complex space formM
n
(c), c≠0, and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field
induced on the hypersurface.
Supported by Grant for the Institute of Mathematics, the University of Tsukuba, and TGRC-KOSEF (1993). 相似文献
3.
Yaning Wang 《Comptes Rendus Mathematique》2018,356(7):823-829
In this paper, we prove that there are no conformally flat real hypersurfaces in nonflat complex space forms of complex dimension two provided that the structure vector field is an eigenvector field of the Ricci operator. This extends some recent results by Cho (Conformally flat normal almost contact 3-manifolds, Honam Math. J. 38 (2016) 59–69) and Kon (3-dimensional real hypersurfaces with η-harmonic curvature, in: Hermitian–Grassmannian Submanifolds, Springer, Singapore, 2017, pp. 155–164). 相似文献
4.
5.
Integral curves of characteristic vector fields of real hypersurfaces in nonflat complex space forms
In this paper, we study real hypersurfaces all of whose integral curves of characteristic vector fields are plane curves in
a nonflat complex space form.
相似文献
6.
We characterize all totally η-umbilic hypersurfaces and ruled real hypersurfaces in nonflat complex space forms and certain real hypersurfaces of type
(A2) in complex projective spaces by using the property that some of their geodesics are mapped to circles of the same curvature
in these ambient spaces. 相似文献
7.
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
8.
Franki Dillen 《Israel Journal of Mathematics》1991,75(2-3):193-202
We show that a semi-parallel hypersurface of a sphere and a hyperbolic space is either flat, parallel or a rotation hypersurface
whose profile curve is a helix.
Supported by a research fellowship of the Research Council of the Katholieke Universiteit Leuven. 相似文献
9.
For hypersurfaces with regular Weingarten operator in nonflat space forms we study the relations between the intrinsic geometry of the third fundamental form metric and the extrinsic geometry of the hypersurface. We prove a theorema-egregium-type result for this metric and, in particular, give a local classification of hypersurfaces in case of an Einstein structure of this metric.Partially supported by the project 19701003 of NSFC.The geometry groops at TU Berlin and KU Leuven cooperate within the GA DGET program. 相似文献
10.
In this paper we determine the real hypersurfaces for which the structure Jacobi operator commutes over both the Ricci tensors
and structure tensors (for a definition of the operator see Sect. 1). We prove that such hypersurfaces are homogneous real
hypersurfaces of type (A) and are a special class of Hopf hypersurfaces. 相似文献
11.
Miguel Ortega Juan de dios Pérez Young Jin Suh 《Czechoslovak Mathematical Journal》2000,50(3):531-537
We characterize real hypersurfaces with constant holomorphic sectional curvature of a non flat complex space form as the ones which have constant totally real sectional curvature. 相似文献
12.
In this paper, we investigate the nonnegative sectional curvature hypersurfaces in a real space form M n+1(c). We obtain some rigidity results of nonnegative sectional curvature hypersurfaces M n+1(c) with constant mean curvature or with constant scalar curvature. In particular, we give a certain characterization of the Riemannian product S k (a) × S n-k (√1 ? a 2), 1 ≤ k ≤ n ? 1, in S n+1(1) and the Riemannian product H k (tanh2 r ? 1) × S n-k (coth2 r ? 1), 1 ≤ k ≤ n ? 1, in H n+1(?1). 相似文献
13.
Sharief Deshmukh 《Monatshefte für Mathematik》2012,121(2):93-106
In this paper, we show that an n-dimensional connected non-compact Ricci soliton isometrically immersed in the flat complex space form
){(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle )}, with potential vector field of the Ricci soliton is the characteristic vector field of the real hypersurface is an Einstein
manifold. We classify connected Hopf hypersurfaces in the flat complex space form
(C
á
ñ\fracn+12,J,
á ,
ñ ){(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle )} and also obtain a characterization for the Hopf hypersurfaces in
(C\fracn+12,J,
á ,
ñ ) {(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle ) }. 相似文献
14.
Sharief Deshmukh 《Monatshefte für Mathematik》2012,166(1):93-106
In this paper, we show that an n-dimensional connected non-compact Ricci soliton isometrically immersed in the flat complex space form ${(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle )}$ , with potential vector field of the Ricci soliton is the characteristic vector field of the real hypersurface is an Einstein manifold. We classify connected Hopf hypersurfaces in the flat complex space form ${(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle )}$ and also obtain a characterization for the Hopf hypersurfaces in ${(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle ) }$ . 相似文献
15.
SHARIEF DESHMUKH 《Proceedings Mathematical Sciences》2012,122(4):629-634
In this paper we are interested in obtaining a condition under which a compact real hypersurface of a complex projective space CP n is a geodesic sphere. We also study the question as to whether the characteristic vector field of a real hypersurface of the complex projective space CP n is harmonic, and show that the answer is in negative. 相似文献
16.
17.
Given a real hypersurface of a complex hyperbolic space #x2102;?H n ,we construct a principal circle bundle over it which is a Lorentzian hypersurface of the anti-De Sitter space H 1 2n+1 .Relations between the respective second fundamental forms are obtained permitting us to classify a remarkable family of real hypersurfaces of ?H n . 相似文献
18.
19.
20.
Yaning Wang 《Mathematische Nachrichten》2021,294(1):195-206
Let M be a Hopf hypersurface in a nonflat complex space form , , of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces of dimension three. By means of this result, we give some new characterizations of Hopf hypersurfaces of type (A) and (B) which generalize those in [14, 18, 26]. 相似文献