Contact hypersurfaces of a complex hyperbolic space. (English) Zbl 0636.53060
It is shown that complete connected contact hypersurfaces of \({\mathbb{C}}H^ n(-4)\) (complex hyperbolic space with Bergman metric), \(n\geq 3\), are congruent to totally geodesic hypersurfaces, horospheres or tubes of positive radii around totally geodesic n-dimensional real hyperbolic space forms imbedded in \({\mathbb{C}}H^ n(-4)\). The author uses the congruence results of his paper “Some families of isoparametric hypersufaces and rigidity in a complex hyperbolic space” (to appear).
Reviewer: Z.Olczak
MSC:
| 53C40 | Global submanifolds |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
References:
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