In this study, the parametric equation of hypersurfaces passing through spacelike and timelike curves that has non-null Frenet vectors in E_1^4 Lorentz Minkowski space was expressed with help curve is frame. Furthermore, hypersurface families were created by giving necessary sufficient conditions so on common isoasymptotic hypersurface. Then, these obtained deviation marching-scale functions si...

A well known result of Forstnerić [18] states that most real-analytic strictly pseudoconvex hypersurfaces in complex space are not holomorphically embeddable into spheres of higher dimension. A more recent result by Forstnerić [19] states even more: most real-analytic hypersurfaces do not admit a holomorphic embedding even into a merely algebraic hypersurface of higher dimension, in particular,...

We complete a classification of junctions of two Friedmann-RobertsonWalker space-times bounded by a spherical thin wall. Our analysis covers super-horizon bubbles and thus complements the previous work of Berezin, Kuzumin and Tkachev. Contrary to sub-horizon bubbles, various topology types for super-horizon bubbles are possible, regardless of the sign of the extrinsic curvature. We also derive ...

Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.

The moduli space of generalized deformations of a Calabi-Yau hypersurface is computed in terms of the Jacobian ring of the defining polynomial. The fibers of the tangent bundle to this moduli space carry algebra structures, which are identified using subalgebras of a deformed Jacobian ring.

We give a Hamiltonian definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We show that our definition provides a geometric invariant for a spacelike hypersurface embedded in a space-time.

We give a Hamiltonian definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We show that our definition provides a geometric invariant for a spacelike hypersurface embedded in a space-time.

A Hamiltonian framework for 2+1 dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically at context. It is shown that the total energy of the system is non-negative, vanishing if and only if space-time is (globally) Minkowskian. Furthermore, contrary to one's experience with usual eld theories, the Hamiltonian is bounded from above. Thi...