Holomorphic and harmonic maps between complete almost Kähler manifolds (Q1119918)

Let M and N be compact almost Kähler manifolds, and \(\phi\) a map from M into N. Lichnérowicz's homotopy theorem says that the difference \(K( )=E'( )-E''( )\) between the holomorphic energy and anti-holomorphic one is a smooth homotopy invariant. In this paper, a non-compact complete domain manifold M is considered, and the author proves that K( ) is an \(L^ 2\)-bounded homotopy invariant. Hence the author also proves the following theorem: Let M, N be complete almost Kähler manifolds. Then an \(L^ 2\)-bounded (anti-) holomorphic map \(\phi\) : \(M\to N\) minimizes the energy function in its \(L^ 2\)-bounded homotopy.