Some conditions on the Weingarten endomorphism of real hypersurfaces in quaternionic space forms

Abstract

We classify the real hypersurfaces in a non-flat quaternionic space form satisfying several conditions on their Weingarten endomorphism. Firstly, we study on the maximal quaternionic distribution of the real hypersurface a relationship between a certain metric tensor and the restriction of the metric of the ambient manifold. Secondly, we consider some formulae relating the Weingarten endomorphism to the curvature operator.