Addendum to “Complete rotation hypersurfaces with <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> constant in space forms”*

Here we study complete rotation hypersurfaces with constant k-th mean curvature H_k in even and 2 < k < n. We prove the existence of a constant such that there are no such hypersurfaces for . We have only one compact hypersurface of this kind with . For each there is a corresponding family of complete immersed rotation hypersurfaces, each family containing two isoparametric hypersurfaces. For H_k ≥ 0, there is also such a family, now containing only one isoparametric hypersurface. Finally, we prove the existence of compact hypersurfaces with arbitrarily large H_k , neither isometric to a sphere nor to a product of spheres. *Bull. Braz. Math. Soc. 30 (2), 1999, 139–161. **Partially supported by FUNCAP, Brazil. ***Partially supported by CNPq, Brazil and DGAPA-UNAM, México.     

On a theorem by Hsiang and Yu

In 1841, Delaunay classified surfaces of revolution with constant mean curvature in the Euclidean three space. As a byproduct of his result, one obtains: A surface of revolution has a periodic generating curve if and only if its mean curvature is non-zero. One hundred and forty years after Delaunay’s work, Hsiang and Yu extended this result to higher dimensions, by extending Delaunay’s idea of tracing the locus of a focus by rolling a given conic section along a line. In this paper, we give a new proof of their result using elementary ODE theory to obtain the periodicity of the solutions under consideration.      

E^n+1中闭超曲面上λ_1^r^L的上界估计

本文研究E^n＋1的中闭超曲面上的Lr（0≤r≤n）算子，得到其第一非零特征值心的两个上界估计，改进和推广了Alias等人的相应结论。     

Statistical properties of the energies and electric dipole moments of the bound vibrational states of the system HCO/COH

From the ab initio calculated three-dimensional adiabatic double-minimum potential energy surface of the HCO⁺/COH⁺ system and the corresponding dipole moment surface the energies of all bound vibrational states and their effective dipole moments are determined applying the Suttcliffe–Tennyson Hamiltonian for triatomic molecules. The energy and dipole data are analysed in terms of statistical methods such as the density of states approach and the nearest-neighbor level spacing distribution (NNSD). Special effort is put into investigating the effect of the tunnelling motion across the isomerization barrier on the NNSD representations.     

球面中等参超曲面及其焦流形的有限性定理

球面中等参超曲面理论近期获得蓬勃发展,它们在等距意义下的分类至今未完全解决,将证明球面中等参超曲面及其焦流形的微分同胚型有限.     

S~4中等参超曲面的谱刻画

本文证明了如果Ｓ４中的具常平均曲率ｈ的超曲面Ｍ与其具平均曲率ｈ的等参超曲面Ｍ０（强）等谱，则Ｍ＝Ｍ０．     

Blaschke isoparametric hypersurfaces in the conformal space ℚ 1 n+1 , I

Let x : M → Q₁ⁿ⁺¹ be a regular hypersurface in the conformal space Q₁ⁿ⁺¹. We classify all the space-like Blaschke isoparametric hypersurfaces with two distinct Blaschke eigenvalues in the conformal space up to the conformal equivalence.     

具有平行的共形第二基本形式的类时超曲面

在文[Classification of type I time-like Hyperspaces with parallel conformal second fundamental forms in the conformal space,Acta Mathematica Sinica,Chinese Series,2011,54(1):125-136]中,我们已对共形空间中具有平行的共形第二基本形式的I型类时超曲面作了分类,本文将探讨其他类型的类时超曲面并完全分类共形空间中具有平行的共形第二基本形式的类时超曲面.