Bilinear forms of K\"ahlerian twistor spinors

Abstract

Generalization of twistor spinors to K\"ahler manifolds which are called K\"ahlerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of K\"ahlerian twistor spinors. We show that the bilinear form equation reduces to K\"ahlerian conformal Killing-Yano equation under special conditions. We also investigate the special cases of holomorphic and anti-holomorphic K\"ahlerian twistor spinors and the bilinear forms of alternative definitions for K\"ahlerian twistor spinors.