K"ahlerian submersions with vanishing Bochner curvature tensor

Abstract

In this paper, we discuss the K"ahlerian submersion with vanishing Bochner curvature tensor and prove that the Bochner curvature tensor of the base space vanishes. Also, we seek a sufficient condition with respect to the length of the Ricci tensor of each fiber that the Bochner curvature tensor of each fiber vanishes.