PSEUDOSYMMETRY PROPERTIES OF GENERALISED WINTGEN IDEAL LEGENDRIAN SUBMANIFOLDS

Abstract

For Legendrian submanifolds $M^n$ in Sasakian space forms $\tilde M^{2n+1}(c)$, Mihai obtained
an inequality relating the the normalised scalar curvature (intrinsic invariant) and the squared mean curvature and the normalised scalar normal curvature of $M$ in the ambient space
$\tilde M$ (extrinsic invariants) which is called the {\it generalised Wintgen inequality}, characterising also the corresponding equality case.
And a Legendrian submanifold $M^n$ in  Sasakian space forms $\tilde M^{2n+1}(c)$ is said to be {\it generalised Wintgen
ideal Legendrian submanifold} of $\tilde M^{2n+1}(c)$ when it realises at
everyone of its points the equality in such inequality. Characterisations based on some basic intrinsic symmetries involving the Riemann--Cristoffel curvature tensor,
the Ricci tensor and the Weyl conformal curvature tensor belonging to the class of {\it pseudosymmetries in the sense of Deszcz} of such {\it generalised Wintgen ideal
Legendrian submanifolds} are given.