Totally geodesic maps into metric spaces |
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Authors: | S-i Ohta |
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Institution: | (1) Mathematical Institute, Tohoku University, Sendai 980-8578, Japan (e-mail: s99m08@math.tohoku.ac.jp) , JP |
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Abstract: | We prove that a totally geodesic map between a Riemannian manifold and a metric space can be represented as the composite
of a totally geodesic map from a Riemannian manifold to a Finslerian manifold and a locally isometric embedding between metric
spaces. As a corollary, we obtain the homotheticity of a totally geodesic map from an irreducible Riemannian manifold to an
Alexandrov space of curvature bounded above. This is a generalization of the case between Riemannian manifolds.
Mathematics Subject Classification (2000): 53C20, 53C22, 53C24
Received: 14 March 2002; in final form: 6 May 2002 / / Published online: 24 February 2003 |
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Keywords: | |
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