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On strongly pseudoconvex manifolds with one-dimensional exceptional set

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Let X be a strongly pseudoconvex n-dimensional manifold with one-dimensional connected exceptional set S. Here we show that if S is reducible, then X is embeddable into CN ×P m for some N, m and in particular X is Kählerian with a possible exception for n = 3; we analyze this exceptional case but we do not know if it may occur. The case in which S is irreducible was previously analyzed by Tan [11], who proved that X is embeddable if either n ≠ 3 or S is not isomorphic to P 1. In the same paper, Tan gave an example of a non-embeddable and non-Kählerian strongly pseudoconvex three-dimensional manifold withP 1 as an exceptional set.

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  1. Department of Mathematics, University of Trente, 38050, Povo (TN), Italy

    E. Ballico

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  1. E. Ballico
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Ballico, E. On strongly pseudoconvex manifolds with one-dimensional exceptional set. J Geom Anal 9, 175–178 (1999). https://doi.org/10.1007/BF02921934

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  • DOI: https://doi.org/10.1007/BF02921934

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