∂∂¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\bar{\\partial }$$\\end{document}-lemma and p-Kähler structures on families of solvmanifolds

Abstract

We provide families of compact (n+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n + 1)$$\\end{document}-dimensional complex non Kähler manifolds satisfying the ∂∂¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\bar{\\partial }$$\\end{document}-Lemma, with holomorphically trivial canonical bundle, carrying a balanced metric and with no p-Kähler structures. Such a construction extends to the completely solvable case in any dimension Nakamura’s construction of low-dimensional holomorphically parallelizable solvmanifolds.