Subscalar pairs of metrics and hypersurfaces with a nondegenerate second fundamental form

Normal Forms of Real Hypersurfaces with Nondegenerate Levi Form

We present a proof of the existence and uniqueness theorem of a normalizing biholomorphic mapping to Chern-Moser normal form. The explicit form of the equation of a chain on a real hyperquadric is obtained. There exists a family of normal forms of real hypersurfaces including Chern-Moser normal form. 0. Introduction Let M be an analytic real hypersurface with nondegenerate Levi form in a comple...

Hypersurfaces of a Sasakian space form with recurrent shape operator

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

On Submanifolds with Tamed Second Fundamental Form

Based on the ideas of Bessa-Jorge-Montenegro [4] we show that a complete submanifold M with tamed second fundamental form in a complete Riemannian manifold N with sectional curvature KN ≤ κ ≤ 0 are proper, (compact if N is compact). In addition, if N is Hadamard then M has finite topology. We also show that the fundamental tone is an obstruction for a Riemannian manifold to be realized as subma...

Computing zeta functions of sparse nondegenerate hypersurfaces

Using the cohomology theory of Dwork, as developed by Adolphson and Sperber, we exhibit a deterministic algorithm to compute the zeta function of a nondegenerate hypersurface defined over a finite field. This algorithm is particularly well-suited to work with polynomials in small characteristic that have few monomials (relative to their dimension). Our method covers toric, affine, and projectiv...