On a Class of Gradient Almost Ricci Solitons
| Autor: | Sinem Güler |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Static spacetime General Mathematics Walker manifold Manifold Standard static spacetime metric Gradient Ricci soliton Differential Geometry (math.DG) 53C21 \and 53C50 \and 53C25 Product (mathematics) Metric (mathematics) FOS: Mathematics Sectional curvature Nabla symbol Mathematics::Differential Geometry Half-conformally flat manifold Constant (mathematics) Signature (topology) Mathematics Ricci soliton Gradienth-almost Ricci soliton |
| Popis: | In this study, we provide some classifications for half-conformally flat gradient f-almost Ricci solitons, denoted by (M, g, f), in both Lorentzian and neutral signature. First, we prove that if $$||\nabla f||$$ is a non-zero constant, then (M, g, f) is locally isometric to a warped product of the form $$I \times _{\varphi } N$$ , where $$I \subset \mathbb {R}$$ and N is of constant sectional curvature. On the other hand, if $$||\nabla f|| = 0$$ , then it is locally a Walker manifold. Then, we construct an example of 4-dimensional steady gradient f-almost Ricci solitons in neutral signature. At the end, we give more physical applications of gradient Ricci solitons endowed with the standard static spacetime metric. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|