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A POINTWISE INEQUALITY IN SUBMANIFOLD THEORY

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*P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken*

**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