On affine symmetries in 4-dimensional spaces of neutral signature

Key Points

• The existence of affine symmetries in 4-dimensional spaces with neutral signature is examined, revealing significant connections.
• Holonomy types for spaces with proper affine vector fields are identified, providing crucial insights into their structure.
• The relationship between affine symmetries and Ricci solitons is highlighted, indicating important geometric implications.
• Examples illustrate the findings, emphasizing the richness of the geometrical characteristics in these spaces.