Abstract
We will discuss in this paper homogeneous locally conformally Kähler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey of known results along with some new results and observations; in particular we make a complete classification of 4-dimensional homogeneous and locally homogeneous l.c.K. manifolds in terms of Lie algebras.
Mathematics Subject Classification (2010). Primary 32M10, 53A30; Secondary 53B35.
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© 2015 Springer International Publishing Switzerland
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Hasegawa, K., Kamishima, Y. (2015). Locally Conformally Kähler Structures on Homogeneous Spaces. In: Ochiai, T., Mabuchi, T., Maeda, Y., Noguchi, J., Weinstein, A. (eds) Geometry and Analysis on Manifolds. Progress in Mathematics, vol 308. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-11523-8_13
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DOI: https://doi.org/10.1007/978-3-319-11523-8_13
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-11522-1
Online ISBN: 978-3-319-11523-8
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