Abstract.
A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This manifold is equipped with an almost product structure and a Killing metric in two ways. In the first case Riemannian almost product manifold with nonintegrable structure is obtained, and in the second case – a pseudo-Riemannian one. Each belongs to a 4-parametric family of manifolds, which are characterized geometrically.
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Mekerov, D. Lie Groups as 4-Dimensional Riemannian or Pseudo-Riemannian Almost Product Manifolds with Nonintegrable Structure. J. geom. 90, 165–174 (2008). https://doi.org/10.1007/s00022-008-2105-1
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DOI: https://doi.org/10.1007/s00022-008-2105-1