Maria Helena Noronha

Low codimensional submanifolds of Euclidean space with nonnegative isotropic curvature

In this paper we study compact submanifolds of Euclidean space with nonnegative isotropic curvature and low codimension. We determine their homology completely in the case of hypersurfaces and for some low codimensional conformally flat immersions.

A splitting theorem for complete manifolds with nonnegative curvature operator

It is shown that any complete, noncompact, simply connected Riemannian manifold with nonnegative curvature operator is isometric to the product of its compact soul (in the sense of Cheeger-Gromoll) and a complete manifold diffeomorphic to a Euclidean space

Some compact conformally flat manifolds with non-negative scalar curvature

In this paper we study some compact locally conformally flat manifolds with a compatible metric whose scalar curvature is nonnegative, and in particular with nonnegative Ricci curvature. In the last section we study such manifolds of dimension 4 and scalar curvature identically zero.

Nonnegatively curved submanifolds in codimension two

Let M be a complete noncompact manifold with nonnegative sectional curvatures isometrically immersed in Euclidean spaces with codimension two. We show that M is a product over its soul, except when the soul is the circle S 1 or M is 3-dimensional and the soul is the Real Projective Plane. We also give a rather complete description of the immersion, including the exceptional cases

Manifolds with pure non-negative curvature operator

We prove that if a simply connected compact Riemannian manifold has pure non negative curvature operator then its irreducible components (in the de Rham decomposition) are homeomorphic to spheres.

Homogeneous Submanifolds of Codimension Two

We study codimension 2 homogeneous submanifolds of Euclidean space for which the index of minimum relative nullity is small. We prove that if minx∈Mνf(x)≤n-5, where ν(x) denotes the nullity of the second fundamental form of the immersion f at the point x, then the manifold Mn is either isometric to a sphere or to a product of two spheres S2×Sn−2 or covered by the Riemannian product Sn−1 ×R. As a consequence, we obtain a classification of compact codimension 2 homogeneous submanifolds of dimension at least 5.

Conformal flatness, cohomogeneity one and hypersurfaces of revolution*

Abstract In this paper we prove that compact conformally flat cohomogeneity one hypersurfaces of Rn + 1. n ⩾ 4, are hypersurfaces of revolution except for a family of counter-examples that we describe in detail.

A note on the first Betti number of submanifolds with nonnegative Ricci curvature in codimension two

AbstractWe show that a complete submanifold in codimension two with nonnegative Ricci curvature which contains no lines and is covered by

Conformally flat immersions in codimension two

\bar M \times R