Group actions, non-Kähler complex manifolds and SKT structures

Poddar , Mainak
Singh Thakur , Ajay
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.
Complex Manifolds


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Ilbıra, Sabahattin; Korkmaz, Mustafa; Department of Mathematics (2017)
A finite rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map defined on this subcomplex into the curve complex is induced from an automorphism of curve complex. In this thesisi we find finite rigid sets in the curve complexes of connected, non-orientable surfaces of genus g with n holes, where g+n neq 4. 
On plateaued functions, linear structures and permutation polynomials
Mesnager, Sihem; Kaytancı, Kübra; Özbudak, Ferruh (2019-01-01)
We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some app...
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: