On the intrinsic Deszcz symmetries and the extrinsic Chen character of Wintgen ideal submanifolds

Abstract

In this paper it is shown that all Wintgen ideal submanifolds in ambient real space forms are Chen submanifolds. It is also shown that the Wintgen ideal submanifolds of dimension $ >3 $ in real space forms do intrinsically enjoy some curvature symmetries in the sense of Deszcz of their Riemann--Christoffel curvature tensor, of their Ricci curvature tensor and of their Weyl conformal curvature tensor.