Zeros of homothetic vector fields in 4-dimensional manifolds of neutral signature

Hall G., Kırık Rácz B.

Journal of Geometry and Physics, vol.203, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 203
  • Publication Date: 2024
  • Doi Number: 10.1016/j.geomphys.2024.105239
  • Journal Name: Journal of Geometry and Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Fixed points, Homotheties, Neutral signature, Symmetries
  • Marmara University Affiliated: Yes

Abstract

This paper explores the situation regarding the zeros of a proper homothetic vector field X on a 4-dimensional manifold admitting a metric of neutral signature. The types of such zeros are described in terms of the algebraic types of the Ricci tensor and Weyl tensor at the said zero together with a geometrical description of the set of such zeros. A comparison is made between the situation occurring here and that for positive definite and Lorentz signatures. Examples are given to show that many of the theoretical possibilities derived for such zeros actually exist.