Imaginary Kahlerian Killing spinors I

We describe and to some extent characterize a new family of Kahler spin manifolds admitting non-trivial imaginary Kahlerian Killing spinors.

The Hermitian Laplace Operator on Nearly Kahler Manifolds

The moduli space NK of infinitesimal deformations of a nearly Kahler structure on a compact 6-dimensional manifold is described by a certain eigenspace of the Laplace operator acting on co-closed primitive (1,1) forms. Using the Hermitian Laplace operator and some representation theory, we compute the space NK on all 6-dimensional homogeneous nearly Kahler manifolds. It turns out that the nearly Kahler structure is rigid except for the flag manifold F(1,2)=SU_3/T^2, which carries an 8-dimensional moduli space of infinitesimal nearly Kahler deformations, modeled on the Lie algebra su_3 of the isometry group.

Deformations of Nearly K{a}hler Structures

We study the space of nearly K{a}hler structures on compact 6-dimensional manifolds. In particular, we prove that the space of infinitesimal deformations of a strictly nearly K{a}hler structure (with scalar curvature scal) modulo the group of diffeomorphisms, is isomorphic to the space of primitive co-closed (1,1)-eigenforms of the Laplace operator for the eigenvalue 2scal/5.