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

Hall G., Kırık Rácz B.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 203
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.geomphys.2024.105239
  • Dergi Adı: Journal of Geometry and Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Fixed points, Homotheties, Neutral signature, Symmetries
  • Marmara Üniversitesi Adresli: Evet

Özet

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.