Claude LeBrun, Shin Nayatani, Takashi Nitta
Self-Dual Manifolds with Positive Ricci Curvature
The paper is published: Math. Z. 224, 1 (1997) 49-63

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

Abstract: We prove that the connected sums
${\bf CP}_2\# {\bf CP}_2$ and ${\bf CP}_2\# {\bf CP}_2\# {\bf CP}_2$
admit self-dual metrics
with positive Ricci curvature.
Moreover, every self-dual metric of positive scalar curvature
on ${\bf CP}_2 \#{\bf CP}_2$ is conformal to a metric
with positive Ricci curvature.

Keywords: selfdual metrics, connected sums of complex projective planes, positive Ricci curvature