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The Isometry Group of the 4-Dimensional Oscillator Group | Synapse

March 29, 2026Open Access

The Isometry Group of the 4-Dimensional Oscillator Group

MHM. Ait Ben HaddouUniversité Moulay Ismail de Meknes YAY. AyadUniversité Moulay Ismail de Meknes

Key Points

To identify the isometry group and Ricci transformation associated with left invariant Riemannian metrics on the oscillator group.
Examine left invariant Riemannian metrics on the oscillator group
Calculate the Ricci transformation for each metric
Determine the complete isometry group utilizing geometric analysis
Identified specific structures within the isometry group corresponding to each metric
Established the relationship between the Ricci transformation and the isometry group
Provided insights into the geometric characteristics of the oscillator group

Abstract

For each left invariant Riemannian metric on the oscillator group, we determine the Ricci transformation and the full isometry group.

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Cite This Study

Haddou et al. (Mon,) studied this question.

synapsesocial.com/papers/69c8c115de0f0f753b39ba6a https://doi.org/https://doi.org/10.5802/jolt.1357