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A pointwise inequality in submanifold theory

P. J. De Smet;  F. Dillen;  Leopold C. A. Verstraelen;  L. Vrancken — 1999

Archivum Mathematicum

We obtain a pointwise inequality valid for all submanifolds M n of all real space forms N n + 2 ( c ) with n ≥ 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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