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...

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.

Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P ! M, there is a canonicaìgeneralized measure' on the space A=G of smooth connections on P modulo gauge transformations. This allows one to deene a Hilbert space L 2 (A=G). Here we construct a set of vectors spanning L 2 (A=G). These vectors are described in terms of`spin networks': graphs embedded in M,...

We propose a novel and fast multiscale feature detection and description approach that exploits the benefits of nonlinear scale spaces. Previous attempts to detect and describe features in nonlinear scale spaces such as KAZE [1] and BFSIFT [6] are highly time consuming due to the computational burden of creating the nonlinear scale space. In this paper we propose to use recent numerical schemes...