Paper · Oct 14, 2025

Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons

Mafal Ndiaye Diop, Abdou Bousso, Cheikh Khoule, Ameth Ndiaye

PDF Abstract page

As on arXiv

Abstract

The objective of this paper is to deepen the study of vector fields on hyperbolic spaces that transform them into a Ricci-Bourguignon soliton. Starting from a recent work in which characterizes these fields as Killing fields of a specific shape, we propose a detailed geometric study of their structure and behavior in the dimensions and . In odd dimension we show that the dual form of these vectors are contact forms. This work aims to enrich the understanding of self-similar solutions of the Ricci flow in a more general context.

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper On conformal collineation and almost Ricci solitons (Adara M. Blaga and Bang-Yen Chen, 2022)6Blaga 2022 Clairaut conformal submersions from Ricci solitons (Murat Polat, 2023)8Polat 2023 On some 3-dimensional almost η-Ricci solitons with diagonal metrics (Adara M. Blaga, 2024)7Blaga 2024 Ricci Solitons on the Poincaré upper half plane (Abdou Bousso and Ameth Ndiaye, 2025)1Bousso 2025 Characterizations of Almost Ricci Bourguignon Solitons (Mohammad Aqib, Hemangi Madhusudan Shah and Dhriti Sundar Patra, 2025)3Aqib 2025 Ricci-Yamabe solitons on the Lie group Sol × ℝⁿ (Abdou Bousso and Ameth Ndiaye, 2026)2Bousso 2026 Ricci Solitons, Almost Theta-Yamabe Solitons, and Finite-Order Tensor Symmetries of a Vector Field on Riemannian Manifolds with Rank-One Anisotropic Curvature (Abdou Bousso and Ameth Ndiaye, 2026)4Bousso 2026 η- Hyperbolic Ricci Solitons on the Unit Tangent Bundle of the Hyperbolic Strip (Amadou Sy, Ameth Ndiaye and Ghodratallah Fasihi-Ramandi, 2026)5Sy 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Ricci Solitons on the Poincaré upper half plane

    Abdou Bousso and Ameth Ndiaye PDF

    Topics Almost & η-Ricci solitons · Same authors Abdou Bousso, Ameth Ndiaye · Shared terms “Bourguignon soliton”, “Ricci Bourguignon”, “characterize”

  2. Ricci-Yamabe solitons on the Lie group

    Abdou Bousso and Ameth Ndiaye PDF

    Topics Almost & η-Ricci solitons · Same authors Abdou Bousso, Ameth Ndiaye · Shared terms “vector field”, “characterize”

  3. Characterizations of Almost Ricci Bourguignon Solitons

    Mohammad Aqib, Hemangi Madhusudan Shah and Dhriti Sundar Patra PDF

    Topics Almost & η-Ricci solitons · Shared terms “Bourguignon soliton”, “Ricci Bourguignon”

  4. Ricci Solitons, Almost Theta-Yamabe Solitons, and Finite-Order Tensor Symmetries of a Vector Field on Riemannian Manifolds with Rank-One Anisotropic Curvature

    Abdou Bousso and Ameth Ndiaye PDF

    Topics Almost & η-Ricci solitons · Same authors Abdou Bousso, Ameth Ndiaye · Shared terms “vector field”

  5. Hyperbolic Ricci Solitons on the Unit Tangent Bundle of the Hyperbolic Strip

    Amadou Sy, Ameth Ndiaye and Ghodratallah Fasihi-Ramandi PDF

    Topics Almost & η-Ricci solitons · Same author Ameth Ndiaye · Shared terms “Killing fields”, “vector field”

  6. On conformal collineation and almost Ricci solitons

    Adara M. Blaga and Bang-Yen Chen PDF

    Topics Almost & η-Ricci solitons · Shared terms “vector field”, “Killing”

  7. On some -dimensional almost -Ricci solitons with diagonal metrics

    Adara M. Blaga PDF

    Topics Almost & η-Ricci solitons · Shared terms “vector field”

  8. Clairaut conformal submersions from Ricci solitons

    Murat Polat PDF

    Topics Almost & η-Ricci solitons · Shared terms “vector field”, “Killing”, “characterize”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.