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Riemannian Geometry of Two Families of Tangent Lie Groups

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Abstract

Using vertical and complete lifts, any left invariant Riemannian metric on a Lie group induces a left invariant Riemannian metric on the tangent Lie group. In the present article, we study the Riemannian geometry of tangent bundle of two families of real Lie groups. The first one is the family of special Lie groups considered by J. Milnor and the second one is the class of Lie groups with one-dimensional commutator groups. The Levi–Civita connection, sectional and Ricci curvatures have been investigated.

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Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions which essentially improved the paper. We are grateful to the office of Graduate Studies of the University of Isfahan for their support. This research was supported by the Center of Excellence for Mathematics at the University of Isfahan.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University of Isfahan, Isfahan, 81746-73441, Iran

    F. Asgari & H. R. Salimi Moghaddam

Authors
  1. F. Asgari
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  2. H. R. Salimi Moghaddam
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Correspondence to H. R. Salimi Moghaddam.

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Communicated by Eaman Eftekhary.

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Asgari, F., Salimi Moghaddam, H.R. Riemannian Geometry of Two Families of Tangent Lie Groups. Bull. Iran. Math. Soc. 44, 193–203 (2018). https://doi.org/10.1007/s41980-018-0014-0

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  • DOI: https://doi.org/10.1007/s41980-018-0014-0

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