Alessandrini, Lucia; Bassanelli, Giovanni A balanced proper modification of \(P_ 3\). (English) Zbl 0761.53034 Comment. Math. Helv. 66, No. 4, 505-511 (1991). A proper modification \(M\) of a Kähler manifold is not necessarily Kähler, but there is a conjecture that \(M\) should always be balanced, i.e. there exists a metric on \(M\) such that the trace of the torsion of the Chern connection vanishes. The authors prove: the 3-dimensional Hironaka manifold, constructed from \(\mathbb{C} P^ 3\) by modification, is balanced. Reviewer: A.Aeppli (Minneapolis) Cited in 1 ReviewCited in 3 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds 32Q99 Complex manifolds Keywords:balanced manifolds; Kaehler manifold; Chern connection; Hironaka manifold PDFBibTeX XMLCite \textit{L. Alessandrini} and \textit{G. Bassanelli}, Comment. Math. Helv. 66, No. 4, 505--511 (1991; Zbl 0761.53034) Full Text: DOI EuDML