SPIN STRUCTURES ON COMPACT HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS

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.

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

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Other information

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

References:

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

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Abstract

V originále

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.