Applications of Disaffinity Vectors to Certain Riemannian Manifolds
A disaffinity vector on a Riemannian manifold is a vector field whose affinity tensor vanishes. In this paper, we prove that every disaffinity vector on a compact Riemannian manifold is an incompressible vector field. Then, we discover a sufficient condition for an incompressible vector field to be...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/24/3951 |
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| Summary: | A disaffinity vector on a Riemannian manifold is a vector field whose affinity tensor vanishes. In this paper, we prove that every disaffinity vector on a compact Riemannian manifold is an incompressible vector field. Then, we discover a sufficient condition for an incompressible vector field to be disaffinity. Next, we study trans-Sasakian 3-manifolds whose Reeb vector field is disaffinity and obtain two sufficient conditions for a trans-Sasakian 3-manifold to be homothetic to a Sasakian 3-manifold. Finally, we prove that a complete Riemannian manifold admitting a non-harmonic disaffinity function satisfying the Eikonal equation and a Ricci curvature inequality is isometric to a Euclidean space. |
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| ISSN: | 2227-7390 |