Pinching and nonexistence of stable harmonic maps (Q1107184)

Using the ``Gauss map proof'' of the equivariant sphere theorem in [the reviewer, \textit{H. Karcher} and \textit{E. A. Ruh}, Math. Ann. 211, 7-21 (1974; Zbl 0273.53051)] the author proves that any stable harmonic map F: \(N^ m\to M^ n\) is constant, whenever \(M^ n\) is simply connected, \(n\geq 3\), 0.83-pinched, and N is compact. In the same spirit an extension of a theorem of \textit{Y. Ohnita} [Tôhoku Math. J., II. Ser. 38, 259-267 (1986; Zbl 0585.58012)] is obtained.