Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator Group
In this paper, we study some homogeneity properties of a semi-direct extension of the Heisenberg group, known in literature as the hyperbolic oscillator (or Boidol) group, equipped with the left-invariant metrics corresponding to the ones of the oscillator group. We identify the naturally reductive...
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2025-01-01
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| author | Giovanni Calvaruso Amirhesam Zaeim Mehdi Jafari Moslem Baghgoli |
| author_facet | Giovanni Calvaruso Amirhesam Zaeim Mehdi Jafari Moslem Baghgoli |
| author_sort | Giovanni Calvaruso |
| collection | DOAJ |
| description | In this paper, we study some homogeneity properties of a semi-direct extension of the Heisenberg group, known in literature as the hyperbolic oscillator (or Boidol) group, equipped with the left-invariant metrics corresponding to the ones of the oscillator group. We identify the naturally reductive case by the existence of the corresponding special homogeneous structures. For the cases where these special homogeneous structures do not exist, we exhibit a complete description of the homogeneous geodesics. |
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| id | doaj-art-555bcd264d8d4db28604b98eb90167e1 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-555bcd264d8d4db28604b98eb90167e12025-01-24T13:22:18ZengMDPI AGAxioms2075-16802025-01-011416110.3390/axioms14010061Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator GroupGiovanni Calvaruso0Amirhesam Zaeim1Mehdi Jafari2Moslem Baghgoli3Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Prov. Lecce-Arnesano, 73100 Lecce, ItalyDepartment of Mathematics, Payame Noor University (PNU), Tehran P.O. Box 19395-4697, IranDepartment of Mathematics, Payame Noor University (PNU), Tehran P.O. Box 19395-4697, IranDepartment of Mathematics, Payame Noor University (PNU), Tehran P.O. Box 19395-4697, IranIn this paper, we study some homogeneity properties of a semi-direct extension of the Heisenberg group, known in literature as the hyperbolic oscillator (or Boidol) group, equipped with the left-invariant metrics corresponding to the ones of the oscillator group. We identify the naturally reductive case by the existence of the corresponding special homogeneous structures. For the cases where these special homogeneous structures do not exist, we exhibit a complete description of the homogeneous geodesics.https://www.mdpi.com/2075-1680/14/1/61hyperbolic oscillator groupsemi-direct extensionshomogeneous structureshomogeneous geodesics |
| spellingShingle | Giovanni Calvaruso Amirhesam Zaeim Mehdi Jafari Moslem Baghgoli Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator Group Axioms hyperbolic oscillator group semi-direct extensions homogeneous structures homogeneous geodesics |
| title | Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator Group |
| title_full | Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator Group |
| title_fullStr | Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator Group |
| title_full_unstemmed | Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator Group |
| title_short | Homogeneous Structures and Homogeneous Geodesics of the Hyperbolic Oscillator Group |
| title_sort | homogeneous structures and homogeneous geodesics of the hyperbolic oscillator group |
| topic | hyperbolic oscillator group semi-direct extensions homogeneous structures homogeneous geodesics |
| url | https://www.mdpi.com/2075-1680/14/1/61 |
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