Add to ORKGThe space of totally geodesic maps in each homotopy class [F] from a compact Riemannian manifold M with non-negative Ricci curvature into a complete Riemannian manifold N with no focal points is path-connected. If [F] contains a totally geodesic map, then each map in [F] is energy-minimizing if and only if it is totally geodesic. When N is compact, each map from a product W x M into N is homotopic to a smooth map that's totally geodesic on the M-fibers. These results generalize the classical theorems of Eells-Sampson and Hartman about manifolds with non-positive sectional curvature and are proved using neither a geometric flow nor the Bochner identity. They can be used to extend to the case of no focal points a number of splitting theorems ...
The paper is devoted to the proof of the following Theorem 1.1 LetM be a complete Riemannian manifol...
AbstractWe prove that a minimal immersion of a complete Riemannian manifold M into another complete ...
We prove that a map f : M \u2192 N with finite p-energy, p > 2, from a complete manifold ( M , \u27e...
ABSTRACT: Let g be a riemannian metric on S2 × S2. In this paper we will show that if (S2 × S2, g) c...
SUMMARY.- We obtain a characterization of totally geodesic horizontally conformal maps by a method w...
Given a Riemannian foliation ${\cal F}$ on a Riemannian manifold M with a bundle-like metric, geomet...
Given a Riemannian foliation ${\cal F}$ on a Riemannian manifold M with a bundle-like metric, geomet...
We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly posi...
We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sect...
Abstract. The structure of local and global harmonic morphisms between Rie-mannian manifolds, with t...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
The Cheeger and Gromoll splitting theorem says that in a complete manifold of nonnegative Ricci curv...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
The paper is devoted to the proof of the following Theorem 1.1 LetM be a complete Riemannian manifol...
AbstractWe prove that a minimal immersion of a complete Riemannian manifold M into another complete ...
We prove that a map f : M \u2192 N with finite p-energy, p > 2, from a complete manifold ( M , \u27e...
ABSTRACT: Let g be a riemannian metric on S2 × S2. In this paper we will show that if (S2 × S2, g) c...
SUMMARY.- We obtain a characterization of totally geodesic horizontally conformal maps by a method w...
Given a Riemannian foliation ${\cal F}$ on a Riemannian manifold M with a bundle-like metric, geomet...
Given a Riemannian foliation ${\cal F}$ on a Riemannian manifold M with a bundle-like metric, geomet...
We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly posi...
We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sect...
Abstract. The structure of local and global harmonic morphisms between Rie-mannian manifolds, with t...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
The Cheeger and Gromoll splitting theorem says that in a complete manifold of nonnegative Ricci curv...
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into...
The paper is devoted to the proof of the following Theorem 1.1 LetM be a complete Riemannian manifol...
AbstractWe prove that a minimal immersion of a complete Riemannian manifold M into another complete ...
We prove that a map f : M \u2192 N with finite p-energy, p > 2, from a complete manifold ( M , \u27e...