Pseudosymmetry properties of generalised wintgen ideal legendrian submanifolds


Aleksandar Šebeković, Miroslava Petrović-Torgašev, Anica Pantić




For Legendrian submanifoldsMn in Sasakian space forms ˜M2n+1(c), I. Mihai obtained an inequality relating the normalised scalar curvature (intrinsic invariant) and the squared mean curvature and the normalised scalar normal curvature of M in the ambient space ˜M (extrinsic invariants) which is called the generalised Wintgen inequality, characterising also the corresponding equality case. And a Legendrian submanifold Mn in Sasakian space forms ˜M2n+1(c) is said to be generalised Wintgen ideal Legendrian submanifold of ˜M2n+1(c) when it realises at everyone of its points the equality in such inequality. Characterisations based on some basic intrinsic symmetries involving the Riemann–Cristo el curvature tensor, the Ricci tensor and theWeyl conformal curvature tensor belonging to the class of pseudosymmetries in the sense of Deszcz of such generalised Wintgen ideal Legendrian submanifolds are given.