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 scalar curvature from the intrinsic geometry of $M^n$, and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of $M^n$ in $N^m(c)$.
@article{107688,
author = {P. J. De Smet and F. Dillen and Leopold C. A. Verstraelen and L. Vrancken},
title = {A pointwise inequality in submanifold theory},
journal = {Archivum Mathematicum},
volume = {035},
year = {1999},
pages = {115-128},
zbl = {1054.53075},
mrnumber = {1711669},
language = {en},
url = {http://dml.mathdoc.fr/item/107688}
}
De Smet, P. J.; Dillen, F.; Verstraelen, Leopold C. A.; Vrancken, L. A pointwise inequality in submanifold theory. Archivum Mathematicum, Tome 035 (1999) pp. 115-128. http://gdmltest.u-ga.fr/item/107688/
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