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.
We show that for Wintgen ideal submanifolds in real space forms the
(intrinsic) Ricci principal directions and the (extrinsic) Casorati principal
directions coincide.
For Legendrian submanifolds M n in Sasakian space formsM 2n+1 (c), I. Mihai obtained an inequal-2010 Mathematics Subject Classification. Primary 53B25; Secondary 53C42 Keywords. Legendrian submanifold in Sasakian space forms, generalised Wintgen ideal Legendrian submanifold, pseudosymmetric space, Ricci pseudosymmetric space, manifold with pseudosymmetric Weyl conformal tensor, Choi-Lu plane of the generalised Wintgen ideal Legendrian submanifold
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