Real hypersurfaces with isometric Reeb flow in complex quadrics

2013/01/03 by Jurgen Berndt, Young Jin Suh, Berndt, Jurgen +1 · 1 citation
Mathematics · #53C40 (Primary) 53C55 #53D15 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C40 #msc:53C55 #msc:53D15

paper · pdf · doi:10.48550/arxiv.1301.0411

14 pages

arxiv created 2013/01/03 · arxiv updated 2013/01/04

Abstract

We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Q^m for m > 2. We show that m is even, say m = 2k, and any such hypersurface is an open part of a tube around a k-dimensional complex projective space CP^k which is embedded canonically in Q^2k as a totally geodesic complex submanifold. As a consequence we get the non-existence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex quadrics.

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• Isometric Reeb flow in complex hyperbolic quadrics

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