Real hypersurfaces in the complex hyperbolic quadric with Reeb invariant Ricci tensor

Abstract

. We first give the notion of Reeb invariant Ricci tensor for real hypersurfaces M in the complex quadric Q m ∗ = SO 02 ,m /SO 2 SO m , which is defined by L ξ Ric = 0, where Ric denotes the Ricci tensor of M in Q m ∗ , and L ξ the Lie derivative along the direction of the Reeb vector field ξ = − JN . Next we give a complete classification of real hypersurfaces in the complex hyperbolic quadric Q m ∗ = SO 02 ,m /SO 2 SO m with Reeb invariant Ricci tensor.