SUBMANIFOLDS OF CONSTANT SCALAR CURVATURE IN A HYPERBOLIC SPACE FORM

Hypersurfaces with Constant Scalar Curvature in a Hyperbolic Space Form

Let M be a complete hypersurface with constant normalized scalar curvature R in a hyperbolic space form H. We prove that if R̄ = R + 1 ≥ 0 and the norm square |h| of the second fundamental form of M satisfies nR̄ ≤ sup |h| ≤ n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], then either sup |h| = nR̄ and M is a totally umbilical hypersurface; or sup |h| = n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], and M i...

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Slant submanifolds with prescribed scalar curvature into cosymplectic space form

In this paper, we have proved that locally there exist infinitely many three dimensional slant submanifolds with prescribed scalar curvature into cosymplectic space form M 5 (c) with c ∈ {−4, 4}while there does not exist flat minimal proper slant surface in M 5 (c) with c 6= 0. In section 5, we have established an inequality between mean curvature and sectional curvature of the subamnifold and ...

hypersurfaces with constant mean curvature in a lorentzian space form