We classify all 5-dimensional homogeneous Riemannian manifolds with positive Ricci curvature and among these we determine all Einstein manifolds. A new Einstein metric is found.
Abstract. We make use of the variational properties of the geodesic distance function of a Riemannian manifold and the technique of the "blowing-up" (o-process) on a complex manifold to derive the nonexistence of compact complex analytic subvarieties in a simply connected, complete Hermitian manifold with nonpositive sectional curvature.1. Notation and preliminaries. In this section we introduce the notation and definitions that will be used in the following sections.(i) Let M" be a complete connected Riemannian manifold of dimension n and class C°°. Throughout this note we will indicate by r = the geodesic distance function of M.A/A = the diagonal of the product manifold M X M. For every (p, q) in M \f M we introduce a natural orthonormal frame of
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