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Nonexistence of para-hyperhermitian structures on Inoue surfaces of type $S^0$
Nonexistence conjecture. Inoue surfaces of type $S^0$ do not admit para-hyperhermitian structures at all.
Conjectureopencomplex-surfaces inoue-surfaces para-hyperhermitian-geometryarXiv posted 2 days ago

Nonexistence of para-hyperhermitian structures on Inoue surfaces of type S0S^0S0