Note on the holonomy groups of pseudo-Riemannian manifolds |
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Authors: | A. S. Galaev |
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Affiliation: | 19856. Masaryk University, Masaryk, Czech Republic
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Abstract: | For an arbitrary subalgebra h ? so(r, s) a polynomial pseudo-Riemannian metric of signature (r + 2, s + 2) is constructed, the holonomy algebra of this metric contains h as a subalgebra. This result shows the essential distinction between the holonomy algebras of pseudo-Riemannian manifolds of index greater than or equal to 2 and the holonomy algebras of Riemannian and Lorentzian manifolds. |
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