On Strominger Space Forms

In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be Kähler. The main result of this article is to confirm the conjecture in dimension 2. We also ver...

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Veröffentlicht in:	The Journal of Geometric Analysis 2022-04, Vol.32 (4), Article 141
Hauptverfasser:	Chen, Shuwen, Zheng, Fangyang
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics
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Zusammenfassung:	In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be Kähler. The main result of this article is to confirm the conjecture in dimension 2. We also verify the conjecture in higher dimensions in a couple of special situations.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-022-00882-7