Published January 1, 2024
| Version v1
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Zeros of homothetic vector fields in 4-dimensional manifolds of neutral signature
Creators
- 1. Univ Aberdeen, Inst Math, Aberdeen AB24 3UE, Scotland
- 2. Marmara Univ, Fac Sci, Dept Math, Goztepe Campus, TR-34722 Istanbul, Turkiye
Description
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. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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