We study null hypersurfaces of indefinite Kähler manifolds and by taking the advantages almost complex structure $J$, we select a suitable rigging $\zeta$, which call $J-$rigging, on hypersurface. This enables us to build an associated Hermitian metric $\breve{g}$ ambient space is restricted into non-degenerated $\widetilde{g}$ normalized derive Gauss-Weingarten type formulae for hypersurface $...

Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then we explain what singularities can occur un...

Abstract We prove the following result: Let K be a strictly convex body in Euclidean space ℝ n , ≥ 3, and let L hypersurface which is image of an embedding sphere

It is shown that there exist real analytic real hypersurfaces in C" which cannot be locally holomorphically imbedded in any finite dimensional sphere S2N~l cCM. In [1], Chern and Moser developed a theory of local invariants of real hypersurfaces in complex manifolds. In doing so, they stressed the analogies between pseudoconformal geometry and Riemannian geometry, defining analogues of the Riem...

The positive mass theorem of general relativity to be addressed here states that the total mass of an isolated gravitational system (viewed from spatial infinity, known as the ADM mass) must be non-negative if its local mass density is non-negative everywhere, and in fact the mass is strictly positive unless the space-time is flat. In this essay we are only concerned with the first part of this...