Abstract
Let M be a non-ruled weakly 2-Hopf real hypersurface in a nonflat complex plane whose mean curvature is invariant along the Reeb flow. In this paper, it is proved that M is Levi-flat if and only if M is locally congruent to a strongly 2-Hopf real hypersurface of a special type. As a corollary we present a class of non-ruled Levi-flat real hypersurfaces of dimension three with non-constant mean curvature.
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