Abstract
The object of study are almost paracomplex pseudo-Riemannian manifolds with a pair of metrics associated each other by the almost paracomplex structure. A torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the pair of associated metrics and the corresponding Levi-Civita connections. A Lie group depending on two real parameters is constructed as an example of a four-dimensional manifold of the studied type and the mentioned invariant objects are found in an explicit form.
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Acknowledgements
The author was supported by projects MU19-FMI-020 and FP19-FMI-002 of the Scientific Research Fund, University of Plovdiv Paisii Hilendarski, Bulgaria.
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Manev, M. Invariant Tensors under the Twin Interchange of the Pairs of the Associated Metrics on Almost Paracomplex Pseudo-Riemannian Manifolds. Mediterr. J. Math. 17, 137 (2020). https://doi.org/10.1007/s00009-020-01576-6
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DOI: https://doi.org/10.1007/s00009-020-01576-6