Topology of the space of absolute minima of the energy functional. (English) Zbl 0564.58014

Guest, M. A.

Am. J. Math. 106, 21-42 (1984).

According to a result of J. Eells and J. C. Wood [J. Lond. Math. Soc., II. Ser. 23, 303-310 (1981; Zbl 0432.58012)], if M is a simply connected Kähler manifold and \(\phi\) : \(S^ 2\to M\) is a smooth map such that the homotopy class \([\phi]\in \pi_ 2M\) has a holomorphic representative, then \(\phi\) has minimal energy in its component if and only if it is holomorphic. Starting from this result and using the method of G. Segal [Acta Math. 143, 39-72 (1979; Zbl 0427.55006)] the author treats the case of an energy functional on \(M=C_*^{\infty}(S^ 2,F)\), where F is a complex flag manifold.

Reviewer: F.Klepp

MSC:

58E20

Harmonic maps, etc.

Keywords:

Morse index; connected Kähler manifold; homotopy class; holomorphic representative; energy functional; complex flag manifold