
arXiv: 2305.10768
A Hopf manifold is a compact complex manifold of which the universal covering is C^n\{0}. In this note we show that any Hopf manifold admits a locally conformally Kaehler structure (shortly lcK structure), by constructing a complex analytic family around a Hopf manifold of diagonal type, which admits a lcK potential, and applying a well known fact (due to Ornea and Verbitsky) that the property of lcK potential is preserved under a complex analytic family over a sufficiently small parameter space.
7 pages
Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics
Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics
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