Note on Holomorphic Transformations Preserving the Bochner Curvature Tensor

TL;DR

This paper proves that in 4-dimensional Kaehler manifolds with nonzero Bochner tensor, any holomorphic transformation preserving this tensor must be a homothety, highlighting a rigidity property of such transformations.

Contribution

It establishes a new rigidity result for holomorphic transformations preserving the Bochner tensor in 4-dimensional Kaehler manifolds.

Findings

Holomorphic transformations preserving the Bochner tensor are homotheties.

The result applies specifically to 4-dimensional Kaehler manifolds with nonvanishing Bochner tensor.

Abstract

The following result is proved: Consider a 4-dimensional Kaehler manifold M with nonvanishing Bochner tensor B. Then any holomorphic transformation of M, which preserves B is a homothety.