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Geodesic Vectors and Flat Totally Geodesic Subalgebras in Nilpotent Metric Lie Algebras

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Abstract

We determine geodesics and flat totally geodesic subalgebras in higher-step nilpotent metric Lie algebras of dimension 5. It is surprising that in the nonfiliform metric Lie algebras with 1-dimensional center, the geodesic vectors and flat totally geodesic subalgebras are independent of the choice of the inner product.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Debrecen, Hungary

    A. Al-Abayechi & Á. Figula

Authors
  1. A. Al-Abayechi
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  2. Á. Figula
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Correspondence to A. Al-Abayechi.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 177, Algebra, 2020.

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Al-Abayechi, A., Figula, Á. Geodesic Vectors and Flat Totally Geodesic Subalgebras in Nilpotent Metric Lie Algebras. J Math Sci 275, 660–673 (2023). https://doi.org/10.1007/s10958-023-06707-4

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  • DOI: https://doi.org/10.1007/s10958-023-06707-4

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