Abstract
Given a manifoldM, a Clifford structure of orderm onM is a family ofm anticommuting complex structures generating a subalgebra of dimension 2m of End(T(M)). In this paper we investigate the existence of locally invariant Clifford structures of orderm≥2 on a class of locally homogeneous manifolds. We study the case of solvable extensions ofH-type groups, showing in particular that the solvable Lie groups corresponding to the symmetric spaces of negative curvature carry invariant Clifford structures of orderm≥2. We also show that for eachm and any finite groupF, there is a compact flat manifold with holonomy groupF and carrying a Clifford structure of orderm.
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Communicated by A. Gray
Partially supported by Conicor (Argentina)
Partially supported by grants from Conicet, Conicor, SECYTUNg (Argentina), and I.C.T.P. (Trieste)
Partially supported by grants from Conicet, Conicor, SECYTUNC (Argentina), T.W.A.S and I.C.T.P. (Trieste)
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Barberis, M.L., Dotti Miatello, I.G. & Miatello, R.J. On certain locally homogeneous Clifford manifolds. Ann Glob Anal Geom 13, 289–301 (1995). https://doi.org/10.1007/BF00773661
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DOI: https://doi.org/10.1007/BF00773661