On solvable generalized Calabi-Yau manifolds
It is known that if on a compact \(2n\)-dimensional symplectic manifold \((M,k)\), for which the maps \[ [k]^p:H^{n-p}(M,R)\Rightarrow H^{n+p}(M,R), \quad 0\leq p\leq n \] are isomorphisms, the Hard Lefschetz Condition (HLC) is satisfied. In [\textit{P. Deligne, P. Griffiths, J. Morgan} and \textit{D. Sullivan}, Invent. Math. 29, 245--274 (1975; Zbl 0312.55011)], the authors proved that if \((M,k,J)\) is a compact Kähler manifold then \((M,k)\) satisfies the (HLC). In this paper an example of a 6-dimensional compact symplectic manifold \((M,k)\) is constructed, carrying a structure of a special generalised Calabi-Yau manifold and satisfying (HLC) whose De Rham algebra is formal. It is interesting to see that this manifold is solvable but not nilpotent and its cohomology is larger than the invariant one.
scientific article; zbMATH DE number 5145703