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 ...

Dadas una variedad riemanniana compacta n dimensional (M, g) y una función diferenciable F : M [flecha diestra] [R.sup.k] consideraremos la variedad [??] = {(x, F(x)) [elemento de] M x [R.sup.k] : x [elemento de] M} = ...

Let g be a riemannian metric on [S.sup.2] x [S.sup.2]. In this paper we will show that if ([S.sup.2] x [S.sup.2], g) contains a totally geodesic torus, then [S.sup.2] x [S.sup.2] does not have positive sectional curvature. ...