1683-3414 1814-0807 Владикавказский математический журнал Vladikavkaz Mathematical Journal Южный математический институт - филиал Федерального государственного бюджетного учреждения науки Федерального научного центра «Владикавказский научный центр Российской академии наук» (ЮМИ ВНЦ РАН) Riemann Solitons on Lorentzian pr-Wave Manifolds Римановы солитоны на лоренцевых pr-волновых многообразиях 10.46698/s0610-2042-8837-a 19850 09 2026 28 3 5 16 https://vmj.ru/eng/archive/detail.php?ELEMENT_ID=19886&SECTION_ID=673 Азами Ш. Azami S. azami@sci.ikiu.ac.ir Международный университет им. Имама Хомейни, Казвин 34149-16818, Иран Imam Khomeini International University, Qazvin 34149-16818, Iran In this research, we delve into the study of Riemann solitons within the context of Lorentzian pr-wave manifolds. Our investigation aims to systematically classify all vector fields that are associated with Riemann solitons on these specific manifolds. A significant aspect of our work is to identify which of these vector fields can be categorized as the gradient type. Furthermore, we demonstrate that any vector field that has the potential to be linked with Riemann solitons can be classified into several categories, namely, Ricci bi-conformal, Killing, and Ricci collineation vector fields. This classification not only enhances our understanding of the geometric properties of these manifolds but also sheds light on the intricate relationships between the various types of vector fields and Riemann solitons. The analysis also gives explicit conditions for the steady and non-steady cases. Gradient Riemann solitons occur only in the steady case, while the potential vector fields may additionally be Killing, Ricci collineation, or Ricci bi-conformal vector fields. В данном исследовании мы изучаем римановы солитоны в контексте лоренцевых многообразий типа PR-волн. Наша работа направлена на систематическую классификацию всех векторных полей, ассоциированных с римановыми солитонами на указанных многообразиях. Важным аспектом нашего исследования является выявление тех из них, которые могут быть отнесены к градиентному типу. Кроме того, мы показываем, что любое векторное поле, потенциально связанное с римановыми солитонами, может быть классифицировано по нескольким категориям: биконформное Риччи, киллингово и коллинеационное Риччи. Данная классификация не только углубляет наше понимание геометрических свойств этих многообразий, но и проясняет сложные взаимосвязи между различными типами таких полей и римановыми солитонами. Анализ также дает явные условия для стационарного и нестационарного случаев. Градиентные солитоны Римана возникают только в стационарном случае, в то время как потенциальные векторные поля могут дополнительно быть киллинговскими, коллинеационными Риччи или биконформными Риччи. лоренцевы многообразия PR-волн риманов солитон биконформное Риччи векторное поле Lorentzian pr-wave manifolds Riemann soliton Ricci bi-conformal vector 1 Hamilton, R. S. The Ricci Flow on Surfaces, Contemporary Mathematics, vol. 71, Providence, RI, American Mathematical Society, 1988, pp. 237-262. DOI: 10.1090/conm/071/954419. Hamilton, R. S. The Ricci Flow on Surfaces, Contemporary Mathematics, vol. 71, Providence, RI, American Mathematical Society, 1988, pp. 237-262. DOI: 10.1090/conm/071/954419. 2 Calin, C. and Crasmareanu, M. From the Eisenhart Problem to Ricci Solitons in f-Kenmotsu Manifolds, Bulletin of the Malaysian Mathematical Sciences Society, 2010, vol. 33, no. 3, pp. 361-368. Calin, C. and Crasmareanu, M. 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