New characterizations of real hypersurfaces with isometric Reeb flow in the complex quadric
We prove an integral inequality for compact orientable real hypersurfaces of the complex quadric $Q^n\ (n\ge 3)$ in terms of their shape operator $S$ and Reeb vector field $\xi $. As direct consequences, we obtain new characterizations for real hypersurfaces of $Q^n$ 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.].