Yoshinobu Kamishima
Classification of Bochner Flat Kähler Manifolds by Heisenberg, Spherical CR Geometry
Preprint series: ESI preprints

MSC:

57S25 Groups acting on specific manifolds

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

53C55 Hermitian and Kahlerian manifolds, See also {32Cxx}

Abstract: A Bochner flat K\"ahler manifold
is a K\"ahler manifold with vanishing Bochner
curvature tensor.
We shall give a uniformization of Bochner flat K\"ahler manifolds.
One of the aims of this paper is to give a
correction to the proof of our previous paper \cite{kamishima2}
concerning uniformization of Bochner flat K\"ahler manifolds.
A Bochner flat locally conformal K\"ahler manifold
is a locally conformal K\"ahler manifold with vanishing Bochner
curvature tensor.
We shall apply our result to Bochner flat locally conformal K\"ahler manifolds.

Keywords: Kahler structure, Chern-Moser- Webster curvature tensor, Pseudo Hermitian structure, Heisenberg Lie group, Bochner curvature tensor, Spherical CR-structure, Locally conformal Kahler structure