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.
Totally geodesic orbits of isometries / F. PODESTA'; VERDIANI L.. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - STAMPA. - 16:(1998), pp. 399-412. [10.1023/A:1006510417098]
Totally geodesic orbits of isometries
PODESTA', FABIO;VERDIANI, LUIGI
1998
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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