Address. Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, BELGIUM
E-mail: franki.dillen@wis.kuleuven.ac.be
Abstract. We obtain a pointwise inequality valid for all submanifolds $M^n$ of all real space forms $N^{n+2}(c)$ with $n\ge 2$ and with codimension two, relating its main scalar invariants, namely, its {\bf scalar curvature} from the intrinsic geometry of $M^n$, and its {\bf squared mean curvature} and its {\bf scalar normal curvature} from the extrinsic geometry of $M^n$ in $N^m(c)$.
AMSclassification. 53B25, 53B35, 53A10, 53C42
Keywords. Submanofolds of real space froms, scalar curvature, normal curvature, mean curvature, inequality