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Cubo (Temuco)

versión On-line ISSN 0719-0646


KOIKE, Naoyuki. Examples of a complex hyperpolar action without singular orbit. Cubo [online]. 2010, vol.12, n.2, pp.127-143. ISSN 0719-0646.

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.

Palabras clave : symmetric space; complex hyperpolar action; complex equifocal submanifold.

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