Compact locally conformally pseudo-Kähler manifolds with essential conformal transformations (Q6629690)

The main result of this paper is the construction of Ricci-flat pseudo-Kähler symmetric spaces in signature \((4n, 4n)\) that admit essential holomorphic homotheties. Some examples of compact locally conformally pseudo-Kähler manifolds with an essential conformal group that are locally conformally Ricci-flat (but not conformally flat) are constructed.\N\NThe author also present real versions of these results in signature \((2n, 2n)\) and, more generally, in signature \((2n + k, 2n + \ell)\).\N\NSome open problems that are related to the Lichnerowicz and Lorentzian Lichnerowicz conjectures are posed.