On the intrinsic Deszcz symmetries and the extrinsic Chen character of Wintgen ideal submanifolds (Q2786389)

A Wintgen ideal submanifold in an ambient real space form is a submanifold \(M^n\), of arbitrary dimension \(n\), \(n\geq 2\), in a real space form \(\tilde M^{n+m}(c)\), with arbitrary \(m\), \(m\geq 2\), of curvature \(c\) for which \(\rho=H^2-\rho^\perp +c\) holds at all points \(p\) of \(M^n\). Here \(\rho\) and \(\rho^\perp\) denote the normalised scalar curvature and normalised scalar normal curvature, respectively, while \(H^2\) denotes the squared mean curvature. It is also shown that all Wintgen ideal submanifolds \(M^n\) in ambient real space forms are Chen submanifolds. For \(n>3\), they 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.