On the Ricci tensor of a real hypersurface of quaternionic hyperbolic space
The authors first show that a real hypersurface in a quaternionic hyperbolic space \(QH^m\) \((m\geq 3)\) with at most two distinct principal curvatures at each point is an open subset of a geodesic hypersphere, or of a tube around some totally geodesic quaternionic hyperbolic hyperplane, or of a horosphere in \(QH^m\). They use this result to prove that each pseudo-Einstein resp. almost-Einstein real hypersurface of \(QH^m\) \((m\geq 3)\) is an open part of one of the above model spaces. As a consequence they get that there are no Einstein real hypersurfaces in \(QH^m\). It is already known that in the dual quaternionic projective space there exists an Einstein real hypersurface.
scientific article; zbMATH DE number 1038287