References
- J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math., 395(1989) 132-141.
- J. Berndt, Real hypersurfaces in quaternionic space forms, J. Reine Angew. Math. 419(1991), 9-26.
- J. Berndt and H. Tamaru, Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit, Tohoku Math. J., 56(2004), 163-177. https://doi.org/10.2748/tmj/1113246549
- J. Berndt and L. Vanhecke, Curvature adapted submanifolds, Nihonkai Math. J., 3(1992), 177-185.
- U. Christ, Homogeneity of equifocal submanifolds, J. Differential Geometry, 62(2002), 1-15. https://doi.org/10.4310/jdg/1090425526
- H. S. M. Coxeter, Discrete groups generated by reflections, Ann. of Math., 35(1934), 588-621. https://doi.org/10.2307/1968753
- H. Ewert, A splitting theorem for equifocal submanifolds in simply connected compact symmetric spaces, Proc. of Amer. Math. Soc., 126(1998), 2443-2452. https://doi.org/10.1090/S0002-9939-98-04328-7
- L. Geatti, Invariant domains in the complexfication of a noncompact Riemannian symmetric space, J. of Algebra, 251(2002), 619-685. https://doi.org/10.1006/jabr.2001.9150
- L. Geatti, Complex extensions of semisimple symmetric spaces, manuscripta math., 120(2006), 1-25. https://doi.org/10.1007/s00229-006-0626-1
- O. Goertsches and G. Thorbergsson, On the Geometry of the orbits of Hermann actions, Geom. Dedicata, 129(2007), 101-118. https://doi.org/10.1007/s10711-007-9198-9
- E. Heintze, X. Liu and C. Olmos, Isoparametric submanifolds and a Chevalley type restriction theorem, Integrable systems, geometry, and topology, 151-190, AMS/IP Stud. Adv. Math. 36, Amer. Math. Soc., Providence, RI, 2006.
- E. Heintze, R. S. Palais, C. L. Terng and G. Thorbergsson, Hyperpolar actions on symmetric spaces, Geometry, topology and physics for Raoul Bott (ed. S. T. Yau), Conf. Proc. Lecture Notes Geom. Topology 4, Internat. Press, Cambridge, MA, 1995 pp214-245.
- S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, New York, 1978.
- M. C. Hughes, Complex reflection groups, Communications in Algebra, 18(1990), 3999-4029. https://doi.org/10.1080/00927879008824120
- R. Kane, Reflection groups and Invariant Theory, CMS Books in Mathematics, Springer-Verlag, New York, 2001.
- N. Koike, Submanifold geometries in a symmetric space of non-compact type and a pseudo-Hilbert space, Kyushu J. Math., 58(2004), 167-202. https://doi.org/10.2206/kyushujm.58.167
- N. Koike, Complex equifocal submanifolds and infinite dimensional anti- Kaehlerian isopara-metric submanifolds, Tokyo J. Math., 28(2005), 201-247. https://doi.org/10.3836/tjm/1244208289
- N. Koike, Actions of Hermann type and proper complex equifocal submanifolds, Osaka J. Math., 42(2005), 599-611.
- N. Koike, A splitting theorem for proper complex equifocal submanifolds, Tohoku Math. J., 58(2006), 393-417. https://doi.org/10.2748/tmj/1163775137
- N. Koike, A Chevalley type restriction theorem for a proper complex equifocal submanifold, Kodai Math. J., 30(2007), 280-296. https://doi.org/10.2996/kmj/1183475518
- N. Koike, The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry, arXiv:math.DG/0807.1601v2.
- A. Kollross, A Classification of hyperpolar and cohomogeneity one actions, Trans. Amer. Math. Soc., 354(2001), 571-612.
- T. Oshima and J. Sekiguchi, The restricted root system of a semisimple symmetric pair, Advanced Studies in Pure Math., 4(1984), 433-497.
- R. S. Palais and C.L. Terng, Critical point theory and submanifold geometry, Lecture Notes in Math., 1353, Springer, Berlin, 1988.
- W. Rossmann, The structure of semisimple symmetric spaces, Can. J. Math., 1(1979), 157-180.
- R. Szoke, Complex structures on tangent bundles of Riemannian manifolds, Math. Ann., 291(1991), 409-428. https://doi.org/10.1007/BF01445217
- R. Szoke, Automorphisms of certain Stein manifolds, Math. Z., 219(1995), 357-385. https://doi.org/10.1007/BF02572371
- R. Szoke, Adapted complex structures and geometric quantization, Nagoya Math. J., 154(1999), 171-183. https://doi.org/10.1017/S002776300002537X
- R. Szoke, Involutive structures on the tangent bundle of symmetric spaces, Math. Ann., 319(2001), 319-348. https://doi.org/10.1007/PL00004437
- R. Szoke, Canonical complex structures associated to connections and complexifications of Lie groups, Math. Ann., 329(2004), 553-591. https://doi.org/10.1007/s00208-004-0525-2
- C. L. Terng, Isoparametric submanifolds and their Coxeter groups, J. Differential Geometry, 21(1985), 79-107. https://doi.org/10.4310/jdg/1214439466
- C. L. Terng and G. Thorbergsson, Submanifold geometry in symmetric spaces, J. Differential Geometry, 42(1995), 665-718. https://doi.org/10.4310/jdg/1214457552
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