Real hypersurfaces with isometric Reeb flow in complex quadrics

TL;DR

This paper classifies real hypersurfaces with isometric Reeb flow in complex quadrics, showing they only exist in even dimensions and are tubes around complex projective spaces, with no such hypersurfaces in odd dimensions.

Contribution

It provides a complete classification of real hypersurfaces with isometric Reeb flow in complex quadrics, revealing their structure and non-existence in odd dimensions.

Findings

Such hypersurfaces exist only in even dimensions.

They are open parts of tubes around CP^k in Q^{2k}.

No such hypersurfaces exist in odd-dimensional quadrics.

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.