  From the basic geometry of submanifolds will be recalled what are the
extrinsic principal tangential directions, (first studied by Camille Jordan in
the $18$seventies), and what are the principal first normal directions, (first
studied by Kostadin Trencevski in the $19$nineties), and what are their
corresponding Casorati curvatures. For reasons of simplicity of exposition
only, hereafter this will merely be done explicitly in the case of arbitrary
submanifolds in Euclidean spaces. Then, for the special case of Lagrangian
submanifolds in complex Euclidean spaces, the natural relationships between
these distinguished tangential and normal directions and their corresponding
curvatures will be established.
