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September 10, 2025Open Access

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.

Abstract

The goal of this paper is to examine affine vector fields on 4-dimensional spaces endowed with a metric of signature (+, +,-,-). The existence of affine symmetries is discussed on these spaces and its connection between the holonomy structure is presented. The holonomy types of such spaces admitting proper affine vector fields are obtained and some examples are given. Additionally, several remarks are made regarding the close relationship of symmetries to Ricci solitons.

On affine symmetries in 4-dimensional spaces of neutral signature

Key Points

Abstract

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