The massive nonsymmetric gravitational theory is shown to posses a linearisation instability at purely GR field configurations, disallowing the use of the linear approximation in these situations. It is also shown that arbitrarily small antisymmetric sector Cauchy data leads to singular evolution unless an ad hoc condition is imposed on the initial data hypersurface.

— We prove that a component Λ of the closure of the set of star points on a hypersurface of degree d ≥ 3 in P is linear. Afterwards, we focus on the case where Λ is of maximal dimension and the case where X is a surface. MSC.— 14J70, 14N15, 14N20

Let X be a nonsingular variety defined over an algebraically closed field of characteristic 0, and D be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along D and compare it with the Chern-Schwartz-MacPherson class of the hypersurface complement. Out result establishes a conjecture by Aluffi raised in [Alu12b].

The classical Bernstein Theorem asserts that an entire minimal graph in R must be planar. This theorem was subsequently generalized to higher dimensions by the works of Fleming [10], Almgren [1], DeGiorgi [6], and Simons [23]. The final result states that an entire n-dimensional minimal graph in R must be given by a linear function over R providing that n ≤ 7. On the other hand, nonlinear entir...

We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold in a natural way. We classify nilmanifolds carrying invariant structures of thi...

The massive nonsymmetric gravitational theory is shown to possess a linearization instability at purely GR field configurations, disallowing the use of the linear approximation in these situations. It is also shown that arbitrarily small antisymmetric sector Cauchy data leads to singular evolution unless an ad hoc condition is imposed on the initial data hypersurface. PACS numbers: 04.50.+h, 04...

In this paper we describe a special class of translation surfaces in a pseudo-Galilean space. We analyze translation surfaces having constant Gaussian and mean curvatures, as well as translation Weingarten surfaces. Mathematics Subject Classification: 53A35, 53A40

We consider convex level sets of solutions a class quasilinear elliptic equations. prove weak Harnack inequality for the eigenvalues Weingarten tensor and then obtain quantitative version constant rank theorem.

A criterion for a spacelike hypersurface in a conformally stationary spacetime to be a Cauchy hypersurface is given. The criterion is based on the forward and the backward completeness of a non-reversible Finsler metric associated to the hypersurface.