On the groups of c-projective transformations of complete Kähler manifolds

Abstract

We show that for any complete connected Kähler manifold the index of the group of complex affine transformations in the group of c-projective transformations is at most two unless the Kähler manifold is isometric to complex projective space equipped with a positive constant multiple of the Fubini-Study metric. This establishes a stronger version of the recently proved Yano-Obata conjecture for complete Kähler manifolds.

24 pages; a few more minor corrections; to appear in Annals of Global Analysis and Geometry

References in corpus (1)

• Curvature and the c-projective mobility of Kaehler metrics with hamiltonian 2-forms