Group actions, non-Kähler complex manifolds and SKT structures

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10.1515coma-2018-0002.pdf

Date

2018-2-2

Author

Poddar , Mainak
Singh Thakur , Ajay

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We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds.

Subject Keywords

Non-Kahler, Complex structure, CR-structure, SKT, CYT, Principal bundles, Orbifolds

URI

https://hdl.handle.net/11511/52014

Journal

Complex Manifolds

DOI

https://doi.org/10.1515/coma-2018-0002

Collections

Department of Mathematics, Article

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Citation Formats

M. Poddar and A. Singh Thakur, “Group actions, non-Kähler complex manifolds and SKT structures,” Complex Manifolds, pp. 9–25, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52014.