A splitting theorem for proper complex equifocal submanifolds
Copyright policy )A splitting theorem for proper complex equifocal submanifolds
In [Proc. Am. Math. Soc. 126, 2443--2452 (1998; Zbl 0911.53034)], \textit{H. Ewert} showed that: An equifocal submanifold in a simply connected compact symmetric space is a nontrivial product of two such submanifolds if and only if its Coxeter group is decomposable. In the paper under review the author introduces the notion of a complex Coxeter group associated with a proper complex equifocal submanifold in a symmetric space of non-compact type and proves a splitting result of Ewert-type for a proper complex equifocal submanifold.
complex Coxeter group, Global submanifolds, symmetric spaces, 53C40, Coxeter groups, equifocal submanifolds, anti-Kaehlerian isoparametric, Complex equifocal, Groups acting on specific manifolds, Differential geometry of symmetric spaces
complex Coxeter group, Global submanifolds, symmetric spaces, 53C40, Coxeter groups, equifocal submanifolds, anti-Kaehlerian isoparametric, Complex equifocal, Groups acting on specific manifolds, Differential geometry of symmetric spaces
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