Submanifolds of codimension two attaining equality in an extrinsic inequality

Details Submanifolds of codimension two attaining equality in an extrinsic inequality Submanifolds of codimension two attaining equality in an extrinsic inequality

2008-02-06

arxiv.org/abs/0802.0805v1

Mathematics

Differential Geometry

Scientific paper

We provide a parametric construction in terms of minimal surfaces of the
Euclidean submanifolds of codimension two and arbitrary dimension that attain
equality in an inequality due to De Smet, Dillen, Verstraelen and Vrancken. The
latter involves the scalar curvature, the norm of the normal curvature tensor
and the length of the mean curvature vector.

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