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@article{2285882, author = {Alekseevsky, D. V. and Chrysikos, Ioannis}, article_number = {3}, doi = {http://dx.doi.org/10.1007/s00031-018-9498-1}, language = {eng}, issn = {1083-4362}, journal = {Transformation Groups}, note = {Nevykazovat pro RIV. Afiliace mimo MU.}, title = {SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS}, url = {https://doi.org/10.1007/s00031-018-9498-1}, volume = {24}, year = {2019} }
TY - JOUR ID - 2285882 AU - Alekseevsky, D. V. - Chrysikos, Ioannis PY - 2019 TI - SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS JF - Transformation Groups VL - 24 IS - 3 SP - 659-689 EP - 659-689 PB - Springer SN - 10834362 N1 - Nevykazovat pro RIV. Afiliace mimo MU. UR - https://doi.org/10.1007/s00031-018-9498-1 N2 - 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. ER -
ALEKSEEVSKY, D. V. a Ioannis CHRYSIKOS. SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS. \textit{Transformation Groups}. Springer, 2019, roč.~24, č.~3, s.~659-689. ISSN~1083-4362. Dostupné z: https://dx.doi.org/10.1007/s00031-018-9498-1.
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