We obtain a characterization for a compact Hopf hypersurface in the nearly Kaehler sphere S using a pinching on the scalar curvature of the hypersurface. It has been also observed that the totally geodesic sphere S in S has induced Sasakian structure as a hypersurface of the nearly Kaehler sphere S. M.S.C. 2000: 53C20, 53C45.

The main result of this paper is that a Lorentzian manifold is locally conformally equivalent to a manifold with recurrent lightlike vector field and totally isotropic Ricci tensor if and only if its conformal tractor holonomy admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for semi-Riemannian manifolds of arbitrary signature we prove that the conformal holonomy algebr...

Abstract In the first part of this paper, we consider a partially overdetermined mixed boundary value problem in space forms and generalize main result [11] to case general domains with partial umbilical forms. Precisely, prove that domain admits solution if only rest is also an hypersurface. second Heintze–Karcher–Ros-type inequality for embedded hypersurfaces free lying on horosphere or equid...

We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. characterise surfaces such as either $S$-Willmore surfaces, quasi-umbilical constant mean curvature 3-dimensional space forms or lightlike lightcones. then investigate Bryant's quartic differential this context and show generically is dive...

In this paper, we give a geometric condition for a CR map, which sends a CR non-umbilical Levi non-degenerate hypersurface in Cn+1 into the hyperquadric in Cn+2 with the same signature, to be CR transversal.

The object of the present paper is to study the totally umbilical hypersurfaces of weakly projective symmetric spaces and it is shown that the totally umbilical hypersurfaces of weakly projective symmetric space is also a weakly projective symmetric space.

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...

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in [16], [8], [6], [7]. We then apply the equation to show that the generalized Chen’s conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-p...

In this paper we study n-dimensional compact minimal submanifolds in S with scalar curvature S satisfying the pinching condition S > n(n − 2). We show that for p ≤ 2 these submanifolds are totally geodesic (cf. Theorem 3.2 and Corollary 3.1). However, for codimension p ≥ 2, we prove the result under an additional restrictions on the curvature tensor corresponding to the normal connection (cf. T...