Biharmonic hypersurfaces in Sasakian space forms

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.     

非平坦洛伦兹空间型中η-双调和超曲面的分类

本文对非平坦洛伦兹空间型中形状算子极小多项式的阶数至多为2的η-双调和超曲面进行了完全分类.     

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。     

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.      

Interpolation of characteristic classes of singular hypersurfaces

We show that the Chern–Schwartz–MacPherson class of a hypersurface X in a nonsingular variety M ‘interpolates’ between two other notions of characteristic classes for singular varieties, provided that the singular locus of X is smooth and that certain numerical invariants of X are constant along this locus. This allows us to define a lift of the Chern–Schwartz–MacPherson class of such ‘nice’ hypersurfaces to intersection homology. As another application, the interpolation result leads to an explicit formula for the Chern–Schwartz–MacPherson class of X in terms of its polar classes.     

New Junction Conditions for Signature Change: Null Boundary Proposal

Existing literature on signature change considers the change surface to be space-like. We construct a new model for signature change based on the signature-changing hypersurface in the beginning of the universe being a null hypersurface. This affects most quantum cosmological considerations, since in quantum cosmology, according to the Hartle–Hawking no-boundary proposal, the creation of the Universe occurred along a space-like 3-hypersurface. Based on this assumption, junction conditions for the signature-change hypersurface are derived and the corresponding results are explained. The energy–momentum of the change surface is non-vanishing and the result for pressure of the change surface is in agreement with inflationary scenario.PACS: 98.80. HW     

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.     

A model for free-radical reactions

Using an EHT type Hamiltonian the Heitler-London-VB treatment of the three-centre three-electron problem is simplified such that the interesting features of the potential hypersurfaces of arbitrary three-centre three-electron systems can be obtained simply from the knowledge of atomic orbital energies and overlap integrals. The method is applied to the hypersurfaces of the H₃ system and extensions of the discussion of general radical reactions are indicated.     

Radial Graphs with Constant Mean Curvature in the Hyperbolic Space

The existence is proved of radial graphs with constant mean curvature in the hyperbolic space H ⁿ⁺¹ defined over domains in geodesic spheres of H ⁿ⁺¹ whose boundary has positive mean curvature with respect to the inward orientation.