On Hermitian manifolds whose Chern connection is Ambrose-Singer

On Hermitian manifolds whose Chern connection is Ambrose-Singer

We consider the class of compact Hermitian manifolds whose Chern connection is Ambrose-Singer, namely, it has parallel torsion and curvature. We prove structure theorems for such manifolds.

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Veröffentlicht in:Transactions of the American Mathematical Society 2023-06, Vol.376 (9), p.6681-6707
Hauptverfasser: Ni, Lei, Zheng, Fangyang
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung:We consider the class of compact Hermitian manifolds whose Chern connection is Ambrose-Singer, namely, it has parallel torsion and curvature. We prove structure theorems for such manifolds.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8956