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Geometry of Ricci solitons admitting a new geometric vector field | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 8، دوره 6، شماره 4، 2025، صفحه 361-370 اصل مقاله (385 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2024.23142.1234 | ||
| نویسندگان | ||
| Farzaneh Shamkhali؛ Ghodratallah Fasihi Ramandi* ؛ Shahroud Azami | ||
| Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran | ||
| چکیده | ||
| In the present paper, we introduce a new geometric vector field (it will be called semi-Killing field) on semi-Riemannaian manifolds. A complete classification of semi-Killing vector fields on 3-dimensional Walker manifolds will be derived. Then, we study Ricci solitons admitting this new vector field (called semi-Killing vector field) as their potential. In Riemannain setting, we prove that Ricci solitons with semi-Killing potential vector field are Einstein. Our results show that such Lorentzian solitons have constant scalar curvature. Finally, application of this new structure in theoretical physics has been investigated. | ||
| کلیدواژه‌ها | ||
| Warped product؛ Geometric vector field؛ Riemannian geometry | ||
| مراجع | ||
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[13] A. G. Walker, Canonical form for a Riemannian space with a parallel field of null planes, Quart. J. Math. Oxford Ser. (2), 1 (1950), pp. 69–79. | ||
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