A fixed point formula for compact almost complex manifolds

Abstract

In this paper, using the group structures of the spheres $S^{1}$, $S^{3}$ and the results of Atiyah-Patodi-Singer, Donnelly and Morita, we introduce a fixed point formula for periodic automorphisms of compact almost complex manifolds. Our main result is Theorem 1.3. The theorem is refined for a certain case if the almost complex manifold admits an Einstein-Kähler metric.