The degree of strong nondegeneracy of the bisectional curvature of exceptional bounded symmetric domains

Abstract

In [1], [2] Siu discovered the complex-analyticity of harmonic maps between two Kähler manifolds under some conditions and prove the strong rigidity of compact quotients of irreducible bounded symmetric domains of dimension at least two. Furthermore, he proposed the following conjecture:

Suppose f: N → M is a harmonic map between compact Kähler manifolds and M is a compact quotient of an irreducible symmetric domain. Let r be the maximal rank of df (over IR). Then f is either holomorphic or antiholomorphic provided that r is appropriately large. In [3] Siu confirmed this conjecture for the four classical domains and indicated that the confirmation for the two exceptional domains depends on the computation of the degree of the strong nondegeneracy of the bisectional curvature in the two exceptional cases.