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On certain non-Kahlerian strongly pseudoconvex manifolds

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Abstract

It has been conjectured that strongly pseudoconvex manifoldsX such that its exceptional setS is an irreducible curve can be embedded biholomorphically into some ℂN ×P m . In this paper we show that this is true, with one exception, namely when dimℂ X = 3 and its first Chern classc 1 (K X ¦S) = 0 whereS ≅P 1 andK X is the canonical bundle ofX. On the other hand, we explicitly exhibit such a 3-foldX that is not Kahlerian; also we construct non-Kahlerian strongly pseudoconvex 3-foldX whose exceptional setS is a ruled surface; those concrete examples naturally raise the possibility of classifying non-Kahlerian strongly pseudoconvex 3-folds.

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  1. Department of Mathematics, Suffolk University, Beacon Hill, 02114, Boston, MA

    Vo Van Tan

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  1. Vo Van Tan
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To the memory of my Mother (1923–94)

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Van Tan, V. On certain non-Kahlerian strongly pseudoconvex manifolds. J Geom Anal 4, 233–245 (1994). https://doi.org/10.1007/BF02921549

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