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Totally Geodesic Orbits of Isometries

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Abstract

We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on isometrically by a non-semisimple Lie group with an hypersurface orbit.

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Authors and Affiliations

  1. Istituto di Matematica, Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, I-50100, Firenze, Italy

    F. Podestà & L. Verdiani

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  1. F. Podestà
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  2. L. Verdiani
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Podestà, F., Verdiani, L. Totally Geodesic Orbits of Isometries. Annals of Global Analysis and Geometry 16, 399–412 (1998). https://doi.org/10.1023/A:1006510417098

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