New characterizations of real hypersurfaces with isometric Reeb flow in the complex quadric
Volume 164 / 2021
Colloquium Mathematicum 164 (2021), 211-219
MSC: Primary 53C24, 53C40; Secondary 53C42, 53C55.
DOI: 10.4064/cm8075-12-2019
Published online: 4 September 2020
Abstract
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.].
