On rotation of complex structures. (English) Zbl 1304.53047
Summary: We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkähler metrics and the Spin-rotations of the author [J. Math. Pures Appl. (9) 102, No. 1, 124–152 (2014; Zbl 1326.14107)]. We determine the (polystable) holomorphic bundles which are rotable, i.e., they remain holomorphic when we change a complex structure by a different one in the family.
MSC:
| 53C26 | Hyper-Kähler and quaternionic Kähler geometry, “special” geometry |
| 53C56 | Other complex differential geometry |
Keywords:
hyper-Kähler manifold; hyperholomorphic bundle; Hermitian-Yang-Mills connection; Spin(7)-instantonCitations:
Zbl 1326.14107References:
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