Recent advances in CR (Cauchy-Riemann) geometry have raised interesting fine questions about the regularity of CRmappings between real analytic hypersurfaces. In analogy with the known optimal results about the algebraicity of holomorphic mappings between real algebraic sets, some statements about the optimal regularity of formal CR mappings between real analytic CR manifolds can be naturally c...

We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riema...

An analytic hypersurface of M is a subset V ⊂ M such that for each point x ∈ V there exists an open set Ux ⊂ M containing x and a holomorphic function fx defined on Ux such that V ⊂ Ux is the zero-set of fx. Such an fx is called a local defining function for V near x. The quotient of any two local defining functions around x is a non-vanishing holomorphic function around x. An analytic hypersur...

We use bounds of mixed character sums modulo a square-free integer q of a special structure to estimate the density of integer points on the hypersurface f1(x1) + . . . + fn(xn) = ax k1 1 . . . x kn n for some polynomials fi ∈ Z[X] and nonzero integers a and ki, i = 1, . . . , n. In the case of f1(X) = . . . = fn(X) = X 2 and k1 = . . . = kn = 1 the above hypersurface is known as the Markoff-Hu...

We consider real hypersurfaces $M$ in complex projective space equipped with both the Levi-Civita and generalized Tanaka-Webster connections. For any nonnull number $k$ symmetric tensor field of type (1,1) $L$ on we can define a (1,2) $M$, $L^{(k)}_F$, related to study symmetry skewsymmetry $A^{(k)}_F$ associated shape operator$A$ $M$.

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

SUMMARY Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing orientations shapes, respectively, of geological reflecting surfaces. Commonly, input data set their computation consists fine 3-D grids scalar fields representing either seismic-driven reflectivities (e.g. amplitudes migrated volumes) or mo...

Abstract We investigate the arrangement of hypersurfaces on a nonsingular varieties whose associated logarithmic vector bundle is arithmetically Cohen–Macaulay (for short, aCM), and prove that projective space only smooth complete intersection with Picard rank one admits an aCM bundle. also obtain number results bundles over several specific varieties. As opposite situation we Torelli‐type prob...