A theorem on compact locally conformal kahler manifolds

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We prove that a compact locally conformai Kahler manifold which satisfies either: (1) it has nonpositive conformai invariant μ [2] and its local conformai Kahler metrics have nonnegative scalar curvature or (2) its local conformai Kähler (l.c.K.) metrics have a positive or negative definite Ricci form is a Kähler manifold. We conjecture that every compact l.c.K. manifold which satisfies all the topological restrictions of a Kahler manifold admits some Kahler metric.

Original languageEnglish
Pages (from-to)279-283
Number of pages5
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - Jul 1979

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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