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Cubo (Temuco)  2010 

Examples of a complex hyperpolar action without singular orbit

DOI: 10.4067/S0719-06462010000200009

Keywords: symmetric space, complex hyperpolar action, complex equifocal submanifold.

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Abstract:

the notion of a complex hyperpolar action on a symmetric space of non-compact type has recently been introduced as a counterpart to the hyperpolar action on a symmetric space of compact type. as examples of a complex hyperpolar action, we have hermann type actions, which admit a totally geodesic singular orbit (or a fixed point) except for one example. all principal orbits of hermann type actions are curvature-adapted and proper complex equifocal. in this paper, we give some examples of a complex hyperpolar action without singular orbit as solvable group free actions and find complex hyperpolar actions all of whose orbits are non-curvature-adapted or non-proper complex equifocal among the examples. also, we show that some of the examples possess the only minimal orbit.

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