共查询到10条相似文献,搜索用时 62 毫秒
1.
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
2.
In this paper, we study biconservative hypersurfaces in and . Further, we obtain complete explicit classifications of biconservative hypersurfaces in 4‐dimensional Riemannian space forms with exactly three distinct principal curvatures. 相似文献
3.
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
4.
Yu Fu 《Mathematische Nachrichten》2015,288(7):763-774
We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces . 相似文献
5.
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide
a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the
homogeneous hypersurfaces together with their multiplicities.
相似文献
6.
7.
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
8.
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
9.
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.
10.
Yu Ping SONG 《数学学报(英文版)》2014,(1)
An umbilical free oriented hypersurfacex:M→Rnwith non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form C=i Ciωi=iρ1(Ei(logρ)(r ri)Ei(r))ωi vanishes and Laguerre shape operator S=ρ1(S 1 rid)has constant eigenvalues.Hereρ=i(r ri)2,r=r1+r2+···+rn 1n 1is the mean curvature radius andSis the shape operator ofx.{Ei}is a local basis for Laguerre metric g=ρ2III with dual basis{ωi}and III is the third fundamental form ofx.In this paper,we classify all Laguerre isoparametric hypersurfaces in Rn(n3)with two distinct non-zero principal curvatures up to Laguerre transformations. 相似文献