Publication details

SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS

Authors

ALEKSEEVSKY D. V. CHRYSIKOS Ioannis

Year of publication 2019
Type Article in Periodical
Magazine / Source Transformation Groups
Citation
web https://doi.org/10.1007/s00031-018-9498-1
Doi http://dx.doi.org/10.1007/s00031-018-9498-1
Description We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G=H; g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also the classification of all flag manifolds carrying an invariant metaplectic structure. Then we investigate spin structures on principal torus bundles over ag manifolds F = G/H, i.e., C-spaces, or equivalently simply-connected homogeneous complex manifolds M = G/L of a compact semisimple Lie group G. We study the topology of M and we provide a sufficient and necessary condition for the existence of an (invariant) spin structure, in terms of the Koszul form of F. We also classify all C-spaces which are fibered over an exceptional spin ag manifold and hence are spin.

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