Some estimates of total tension and their applications (Q1819752)

The main result of this paper is an estimate of the total tension \(\int | \Delta f|^ 2\) for maps \(f: M^ n\to {\mathbb{R}}^ n\) in terms of the eigenvalues \(\lambda_ 1\) and \(\lambda_ 2\) of \((M^ n,g)\). As an application sharp inequalities involving only \(\lambda_ 1\) and \(\lambda_ 2\) are obtained for compact minimal submanifolds of rank-one symmetric spaces.