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Special cohomogeneity one isometric actions on irreducible symmetric spaces of types I and II. (English) Zbl 1033.53043
In this paper the author studies isometric actions on compact symmetric spaces for which the principal orbits are tubular hypersurfaces around totally geodesic singular orbits. It is shown that in these cases the symmetric space can be thought of as a compact tube the radius of which is determined by the curvature tensor. A simple method is obtained to determine volumes of symmetric spaces by using volumes of lower dimensional ones. Moreover, the author discusses the classical irreducible symmetric spaces of types I and II, each of which admits such special hyperpolar actions.

MSC:
53C35 Differential geometry of symmetric spaces
53C40 Global submanifolds
57S15 Compact Lie groups of differentiable transformations
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