Group actions, non-Kahler complex manifolds and SKT structures

Poddar M., Thakur A. S.

COMPLEX MANIFOLDS, cilt.5, sa.1, ss.9-25, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1515/coma-2018-0002
  • Dergi Adı: COMPLEX MANIFOLDS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.9-25
  • Anahtar Kelimeler: Non-Kahler, complex structure, CR-structure, SKT, CYT, Principal bundles, Orbifolds, PRINCIPAL BUNDLES, LIE-GROUPS, COMPACT, COMPACTIFICATIONS, CONSTRUCTION, GEOMETRY, TORSION, THEOREM, SPACES
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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 Samel-son and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kahler 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-Kahler) complex structures on tangential frame bundles of complex orbifolds.