×

zbMATH — the first resource for mathematics

A pointwise inequality in submanifold theory. (English) Zbl 1054.53075
Let \(M^n\) be a submanifold of a real space forms \(N^{n+2}(c)\) with \(n\geq 2\) and with codimension two. The authors prove a pointwise inequality relating the scalar curvature, the squared mean curvature and the normal curvature function. Examples of several classes of submanifolds are given realizing this inequality and classification theorems are obtained on various classes of submanifolds realizing the inequality.

MSC:
53C40 Global submanifolds
PDF BibTeX XML Cite
Full Text: EuDML