共查询到20条相似文献,搜索用时 15 毫秒
1.
Miguel Ortega Juan de Dios Pérez Young Jin Suh 《Czechoslovak Mathematical Journal》2006,56(2):377-388
In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space
form M
m
(c), c ≠ 0 as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional
curvature given in [11]. 相似文献
2.
Some geometrical properties of Hopf hypersurfaces of Kähler manifolds are introduced and a special attention is given to the case of hypersurfaces in complex projective spaces. 相似文献
3.
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
4.
5.
The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel. 相似文献
6.
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
7.
We prove that there does not exist any semi-parallel real hypersurface in complex two-plane Grassmannians. With this result, the nonexistence of recurrent real hypersurfaces in complex two-plane Grassmannians can also be proved. 相似文献
8.
We consider the Boothby–Wang fibration of a strictly regular Sasakian space form N and find the characterization of biharmonic Hopf cylinders over submanifolds of . Then, we determine all proper-biharmonic Hopf cylinders over homogeneous real hypersurfaces in complex projective spaces. 相似文献
9.
Oscar Palmas 《Bulletin of the Brazilian Mathematical Society》1999,30(2):139-161
In this paper we classify all complete rotation hypersurfaces withH
k
constant in
n+1 andH
n+1, is the normalizedk-th symmetric function of the principal curvatures. Partial results are also given forH
n+1.Partially supported by DGAPA-UNAM, México, CONACYT, México, under Project 1068P, and CNPp, Brazil. 相似文献
10.
We consider closed biharmonic hypersurfaces in a Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic hypersurfaces in space forms. As an application of this formula, we reobtain a result concerning the closed biharmonic hypersurfaces in Euclidean spheres that lie in a closed hemisphere. 相似文献
11.
We present the motivation and current state of the classification problem of real hypersurfaces with constant principal curvatures in complex space forms. In particular, we explain the classification result of real hypersurfaces with constant principal curvatures in nonflat complex space forms and whose Hopf vector field has nontrivial projection onto two eigenspaces of the shape operator. This constitutes the following natural step after Kimura and Berndt?s classifications of Hopf real hypersurfaces with constant principal curvatures in complex space forms. 相似文献
12.
Jü rgen Berndt José Carlos Dí az-Ramos 《Proceedings of the American Mathematical Society》2007,135(10):3349-3357
We classify real hypersurfaces with constant principal curvatures in the complex hyperbolic plane. It follows from this classification that all of them are open parts of homogeneous ones.
13.
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4‐dimensional space forms (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
15.
José N. Gomes Henrique F. de Lima Fábio R. dos Santos Marco Antonio L. Velásquez 《Journal of Mathematical Analysis and Applications》2014
We deal with complete linear Weingarten spacelike hypersurfaces immersed in a Lorentzian space form, having two distinct principal curvatures. In this setting, we show that such a spacelike hypersurface must be isometric to a certain isoparametric hypersurface of the ambient space, under suitable restrictions on the values of the mean curvature and of the norm of the traceless part of its second fundamental form. Our approach is based on the use of a Simons type formula related to an appropriated Cheng–Yau modified operator jointly with some generalized maximum principles. 相似文献
16.
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
17.
Young Jin Suh 《Acta Mathematica Hungarica》2006,112(1-2):89-102
Summary We introduce the notion of recurrent shape operator for a real hypersurface M in the complex two-plane Grassmannians G2(Cm+2) and give a non-existence property of real hypersurfaces in G2(Cm+2) with the recurrent shape operator. 相似文献
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20.
Yongfan Zheng 《Annals of Global Analysis and Geometry》1995,13(4):317-321
This paper gives the intrinsic conditions for a compact space-like hypersurface in a de Sitter space to be isometric to a sphere. 相似文献