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HOLONOMY AND 3-SASAKIAN HOMOGENEOUS MANIFOLDS VERSUS SYMPLECTIC TRIPLE SYSTEMS

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Abstract

Our aim is to support the choice of two remarkable connections with torsion in a 3-Sasakian manifold, proving that, in contrast to the Levi-Civita connection, the holonomy group in the homogeneous cases reduces to a proper subgroup of the special orthogonal group, of dimension considerably smaller. We realize the computations of the holonomies in a unified way, by using as a main algebraic tool a nonassociative structure, that of a symplectic triple system.

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  1. Department of Applied Mathematics, University of Málaga, 29071, Málaga, Spain

    C. DRAPER

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Dedicated to the memory of Professor Thomas Friedrich

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C. Draper is supported by Junta de Andalucía through projects FQM-336 and UMA18-FEDERJA-119 and by the Spanish Ministerio de Ciencia e Innovación through project PID2019-104236GB-I00, all of them with FEDER funds.

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DRAPER, C. HOLONOMY AND 3-SASAKIAN HOMOGENEOUS MANIFOLDS VERSUS SYMPLECTIC TRIPLE SYSTEMS. Transformation Groups 26, 1293–1314 (2021). https://doi.org/10.1007/s00031-020-09609-w

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