ALEKSEEVSKY, D. V. and Ioannis CHRYSIKOS. SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS. Transformation Groups. Springer, 2019, vol. 24, No 3, p. 659-689. ISSN 1083-4362. Available from: https://dx.doi.org/10.1007/s00031-018-9498-1.
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Basic information
Original name SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS
Authors ALEKSEEVSKY, D. V. and Ioannis CHRYSIKOS.
Edition Transformation Groups, Springer, 2019, 1083-4362.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW URL
Impact factor Impact factor: 0.750
Doi http://dx.doi.org/10.1007/s00031-018-9498-1
UT WoS 000479069800002
Tags RIV ne
Tags International impact, Reviewed
Changed by Changed by: Mgr. Marie Šípková, DiS., učo 437722. Changed: 26/5/2023 11:53.
Abstract
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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