Andrei Moroianu, Uwe Semmelmann
Kaehlerian Killing Spinors, Complex Contact Structures and Twistor Spaces
The paper is published: C. R. Acad. Sci., Paris, Ser. I, 323, 1 (1996) 57-61

MSC:

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

32L25 Twistor theory, double fibrations

53A50 Spinor analysis

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

Abstract: The notion of {\it complex contact structures}
was introduced in the late 50's by S. Kobayashi (cf. [6]), in analogy
to real contact structures.

In 1982 S. Salamon investigated in [9] quaternionic K\"ahler
manifolds. In particular, he defined the
{\it twistor space} over such a manifold as a generalization of the
classical notion of twistor space over a self-dual 4-manifold.

In 1986 K.D. Kirchberg was led to define {\it K\"ahlerian Killing
Spinors}, in order to characterize the K\"ahler spin manifolds of odd
complex dimension admitting the smallest possible eigenvalue of the
Dirac operator (cf. [4]). Some important contributions to this
problem are also due to O. Hijazi (cf. [1]).

The aim of this paper is to explain the close connection between these
three notions.

Keywords: Kaehlerian Killing spinors, complex contact structures, twistor spaces, Sasakian manifolds, complex almost contact structures, complex k-contact structures