On solvable generalized Calabi-Yau manifolds
type: Item
instance of: scholarly article
title: On solvable generalized Calabi-Yau manifolds
zbMATH Open document ID: 1127.53065
author: Paolo De Bartolomeis
author: Adriano Tomassini
publication date: 2007-04-24T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10177
review text: 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.
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 32Q25
zbMATH DE Number: 5145703
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: Calabi-Yau-manifolds
MaRDI profile type: Publication
OpenAlex ID: W2526651442
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DOI: 10.5802/AIF.2213
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5145703