Examples of a complex hyperpolar action without singular orbit
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 sin...
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| Lenguaje: | English |
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2010
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oai:scielo:S0719-064620100002000092018-10-08Examples of a complex hyperpolar action without singular orbitKoike,Naoyuki symmetric space complex hyperpolar action complex equifocal submanifold 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.2 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000200009en10.4067/S0719-06462010000200009 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
symmetric space complex hyperpolar action complex equifocal submanifold |
| spellingShingle |
symmetric space complex hyperpolar action complex equifocal submanifold Koike,Naoyuki Examples of a complex hyperpolar action without singular orbit |
| description |
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. |
| author |
Koike,Naoyuki |
| author_facet |
Koike,Naoyuki |
| author_sort |
Koike,Naoyuki |
| title |
Examples of a complex hyperpolar action without singular orbit |
| title_short |
Examples of a complex hyperpolar action without singular orbit |
| title_full |
Examples of a complex hyperpolar action without singular orbit |
| title_fullStr |
Examples of a complex hyperpolar action without singular orbit |
| title_full_unstemmed |
Examples of a complex hyperpolar action without singular orbit |
| title_sort |
examples of a complex hyperpolar action without singular orbit |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2010 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000200009 |
| work_keys_str_mv |
AT koikenaoyuki examplesofacomplexhyperpolaractionwithoutsingularorbit |
| _version_ |
1714206766215987200 |