New characterizations of real hypersurfaces with isometric Reeb flow in the complex quadric

Abstract

We prove an integral inequality for compact orientable real hypersurfaces of the complex quadric Q (n ≥ 3) in terms of their shape operator S and Reeb vector field ξ. As direct consequences, we obtain new characterizations for real hypersurfaces of Q with isometric Reeb flow. Such hypersurfaces have been classified by J. Berndt and Y. J. Suh [Int. J. Math. 24 (2013), art. 1350050, 18 pp.].