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The conjecture that non-Kähler locally conformally Kähler manifolds cannot admit multiple special Hermitian metrics
Nonexistence conjecture. A compact, non-Kähler, locally conformally Kähler manifold cannot be endowed with various different special Kähler metrics, such as balanced, pluriclosed,…
Conjectureopencomplex-geometry locally-conformally-kahler special-hermitian-geometryarXiv posted 2 days ago

The conjecture that non-Kähler locally conformally Kähler manifolds cannot admit multiple special Hermitian metrics