Let X be the hypersurface of the complex affine four-space a defined by the equation xy + z + t + x = 0. It is well-known that X is an affine contractible smooth threefold, which is not algebraically isomorphic to affine three-space. The main result of this article is to show that there exists another hypersurface Y of a, which is isomorphic to X , but such that there exists no automorphism of ...

where (ζ : z : w) are homogeneous coordinates in CP, the space C is given in CP by ζ 6= 0 with z = z/ζ , w = w/ζ , and the hyperplane at infinity by ζ = 0. If the form 〈z, z〉 is non-degenerate, then Q〈·,·〉 is a non-singular Levi non-degenerate hypersurface, and it is well-known that the following continuation phenomena hold for CR-automorphisms of Q〈·,·〉: (i) every local C-smooth CR-automorphis...

The main purpose of this paper is to study biharmonic hypersurface in a quasi-paraSasakian manifold $\mathbb{Q}^{2m+1}$. Biharmonic hypersurfaces are special cases maps and the critical points bienergy functional. condition biharmonicity for non-degenerate $\mathbb{Q}^{2m+1}$ investigated both cases: either characteristic vector field unit normal or it belongs tangent space hypersurface. Some r...

The Ricci curvature at an isolated singularity of an immersed hypersurface exhibits a local behaviour echoing a global property of the Ricci curvature on a complete hypersurface in euclidean space (i.e., the Efimov theorem [12], that sup Ric ≥ 0). This local behaviour takes the form of a near universal bound on the decay of the Ricci curvature at a simple singularity (eg. a cone singularity) in...

Recently Bousso conjectured the entropy crossing a certain light-like hypersurface is bounded by the surface area. We point out a number of difficulties with this conjecture.

A differential form vanishing on the tangent space at smooth points of a reduced embedded analytic germ is called conormal. For proving that a conormal one–form of a hypersurface vanishes at its singularities we state a Bertini–type theorem.

We compute the number of rational quartics on a general Calabi-Yau hypersurface in weighted projective space P(2, 1). The result agrees with the prediction made by mirror symmetry.

In the Penrose limit, AdS×S space turns into a Cahen-Wallach (CW) space whose Killing vectors satisfy a Heisenberg algebra. I discuss how this algebra is mapped onto the holographic screen on the boundary of AdS. Furthermore, I show that the algebra on the boundary of AdS may be obtained directly from the CW space by appropriately constraining the states defined on it. By viewing the constraint...

In canonical gravity, general covariance is implemented by hypersurface-deformation symmetries on phase space. The different versions of hypersurface deformations required for full have complicated interplays with one another, governed non-Abelian brackets structure functions. For spherically symmetric space-times, it possible to identify a certain Abelian substructure within deformations, whic...

In braneworld models, Space-Time-Matter and other Kaluza-Klein theories, our spacetime is devised as a four-dimensional hypersurface orthogonal to the extra dimension in a fivedimensional bulk. We show that the FRW line element can be “reinvented” on a dynamical four-dimensional hypersurface, which is not orthogonal to the extra dimension, without any internal contradiction. This hypersurface i...