Some families of isoparametric hypersurfaces and rigidity in a complex hyperbolic space

Vernon, Micheal H.

doi:10.1090/S0002-9947-1989-0983871-X

Some families of isoparametric hypersurfaces and rigidity in a complex hyperbolic space
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by Micheal H. Vernon

Trans. Amer. Math. Soc. 312 (1989), 237-256

DOI: https://doi.org/10.1090/S0002-9947-1989-0983871-X

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Abstract:

The geometric notion of equivalence for submanifolds in a chosen ambient space is that of congruence. In this study, a certain type of isoparametric hypersurface of a complex hyperbolic space form is shown to have a rigid immersion by utilizing the congruences of a Lorentzian hyperbolic space form that lies as an ${S^1}$-fiber bundle over the complex hyperbolic space. Several families of isoparametric hypersurfaces (namely tubes and horospheres) are constructed whose immersions are rigid.

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