Curvature-adapted real hypersurfaces in quaternionic space forms

Abstract

In this paper we study geodesics on curvature-adapted real hypersurfaces in non-flat quaternionic space forms. By observing the extrinsic shape of geodesics on these hypersurfaces we characterize them in the class of real hypersurfaces. We also investigate the length spectrum of geodesic spheres, which are the simplest curvature-adapted real hypersurfaces, in non-flat quaternionic space forms.