Complex hyperpolar actions with a totally geodesic orbit
Koike, Naoyuki
Osaka J. Math., Tome 44 (2007) no. 1, p. 491-503 / Harvested from Project Euclid
We first show that homogeneous submanifolds with abelian normal bundle in a symmetric space of non-compact type occur as principal orbits of complex hyperpolar actions on the symmetric space. Next we show that all complex hyperpolar actions with a reflective orbit are orbit equivalent to Hermann type actions. Furthermore, we classify complex hyperpolar actions with a totally geodesic orbit in the case where the ambient symmetric space is irreducible. Also, we list up the cohomogeneities of Hermann type actions on irreducible symmetric spaces.
Publié le : 2007-09-14
Classification:  53C35,  53C40
@article{1189717419,
     author = {Koike, Naoyuki},
     title = {Complex hyperpolar actions with a totally geodesic orbit},
     journal = {Osaka J. Math.},
     volume = {44},
     number = {1},
     year = {2007},
     pages = { 491-503},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1189717419}
}
Koike, Naoyuki. Complex hyperpolar actions with a totally geodesic orbit. Osaka J. Math., Tome 44 (2007) no. 1, pp.  491-503. http://gdmltest.u-ga.fr/item/1189717419/