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Keywords:
submanofolds of real space froms; scalar curvature; normal curvature; mean curvature; inequality
submanofolds of real space froms; scalar curvature; normal curvature; mean curvature; inequality
Summary:
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 $N^m(c)$.
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