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Left invariant degenerate metrics on Lie groups

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Abstract

We consider left invariant degenerate metrics on the group \({{\mathsf{SO}}(3)}\). We prove that the isometry group of such a metric is \({{\mathsf{SO}}(3)}\) itself unless the metric is transversally Riemannian in which case the isometry group has infinite dimension.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, Département de Mathématiques, Faculté des sciences exactes, Université de Bejaia, 06000, Bejaïa, Algeria

    Malika Oussalah & Esmaa Bekkara

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  1. Malika Oussalah
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  2. Esmaa Bekkara
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Correspondence to Malika Oussalah.

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Oussalah, M., Bekkara, E. Left invariant degenerate metrics on Lie groups. J. Geom. 108, 171–184 (2017). https://doi.org/10.1007/s00022-016-0332-4

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  • DOI: https://doi.org/10.1007/s00022-016-0332-4

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