Geodesic
A pointwise inequality in submanifold theory
Archivum mathematicum, Tome 35 (1999) no. 2, pp. 115-128.

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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 $N^m(c)$.
Classification : 53C40
Keywords: submanofolds of real space froms; scalar curvature; normal curvature; mean curvature; inequality 
@article{ARM_1999__35_2_a2,
     author = {De Smet, P. J. and Dillen, F. and Verstraelen, L. and Vrancken, L.},
     title = {A pointwise inequality in submanifold theory},
     journal = {Archivum mathematicum},
     pages = {115--128},
     publisher = {mathdoc},
     volume = {35},
     number = {2},
     year = {1999},
     mrnumber = {1711669},
     zbl = {1054.53075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1999__35_2_a2/}
}
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De Smet, P. J.; Dillen, F.; Verstraelen, L.; Vrancken, L. A pointwise inequality in submanifold theory. Archivum mathematicum, Tome 35 (1999) no. 2, pp. 115-128. http://geodesic.mathdoc.fr/item/ARM_1999__35_2_a2/