Let M [subset] [S.sup.n] be a minimal hypersurface, and let us denote by A the shape operator of M. In this paper we give an alternative proof of the theorem that states that if [[absolute value of A].sup.2] = n - 1, then ...

The present article is devoted to present a new characterization of the Cartan isoparametric hypersurfaces in terms of properties of the polynomial, that determines the algebraic set of planar normal sections on the ...

In this paper we obtain a classification of hypersurfaces in the Euclidean sphere having two principal curvatures; for some of the results we impose that the sectional curvature (Ricci curvature, resp.) is non-negative Ricci.

The present paper contains some results about the algebraic setsof planar normal sections associated to the focal manifolds of homogeneous isoparametric hypersurfaces in spheres. With the usual identication of thetangent ...

We present tools, such as a maximum principle for elliptic functions and properties of a-hyperbolic polynomials, to study a tangency principle between two hypersurfaces with r-mean curvatures of a Riemannian manifold, which ...

Let M n be a complete Riemannian manifold immersed isometrically in the unity Euclidean sphere Sn+1. In [9], B. Smyth proved that if M n , n ≧ 3, has sectional curvature K and Ricci curvature Ric, with inf K > −∞, then sup ...

In this paper we prove that a compact oriented hypersurface of a Euclidean sphere with nonnegative Ricci curvature and infinite fundamental group is isometric to an H(r)-torus with constant mean curvature. Furthermore, we ...