Abstract
In this paper Kählerian Killing spinors on manifolds of complex dimensionm=4l+3 are constructed. The construction is based on a theorem which states that a closed Kähler Einstein manifold of complex dimension 4l+3 and positive scalar curvature admits a Kählerian Killing spinor if and only if there is a complex (2l+1)-contact structure. In particular, any complex contact structure in the usual sense gives rise to such a generalized contact structure. Using this, new examples of Kählerian Killing spinors are obtained.
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Kirchberg, K.D., Semmelmann, U. Complex contact structures and the first eigenvalue of the dirac operator on Kähler manifolds. Geometric and Functional Analysis 5, 604–618 (1995). https://doi.org/10.1007/BF01895834
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DOI: https://doi.org/10.1007/BF01895834