The Isometry Group of the 4-Dimensional Oscillator Group

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