Abstract. In general Riemannian manifolds the shape operators and the curvature endomorphisms with respect to the normal vectors on a given hypersurface not necessarily commute. In this paper examples are presented for submanifolds of codimension one having the above commutativity property. Particularly, tubular hypersurfaces in Riemannian symmetric spaces are discussed.

AMS Subject Classification (1991): 53B25

Received February 19, 1993, and in revised form July 7, 1993. (Registered under 5552/2009.)