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Real hypersurfaces in complex two-plane Grassmannians with \(\xi \)-invariant Ricci tensor. (English) Zbl 1209.53046

Summary: First we introduce the full expression of the Ricci tensor of a real hypersurface \(M\) in complex two-plane Grassmannians \(G_2(\mathbb C^{m+2})\) from the equation of Gauss. Next, we give a new characterization of real hypersurfaces of type \((A)\) in complex two-plane Grassamnnians with a vanishing Lie derivative of the Ricci tensor \(S\) in the direction of the Reeb vector field \(\xi \), that is, an \(\xi \)-invariant Ricci tensor.

MSC:

53C40 Global submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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