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On Non‐Compact Extended Bach Solitons

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  • Rahul Poddar

Abstract

We study the characterization of non‐compact solitons of the extended Bach flow, known as an extended Bach soliton. We prove that a weakly conformally flat extended Bach soliton (Mn,g,V)$(M^n,g,V)$ with harmonic Weyl tensor is Bach‐flat and the potential vector field V$V$ is conformal. In the case of an extended gradient Bach soliton, we impose certain regularity conditions on the potential function, Ricci curvature constraints on M$M$, and assume that the Weyl tensor is harmonic, to deduce that M$M$ is trivial and Bach‐flat.

Suggested Citation

  • Rahul Poddar, 2026. "On Non‐Compact Extended Bach Solitons," Mathematische Nachrichten, Wiley Blackwell, vol. 299(5), pages 1140-1151, May.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:5:p:1140-1151
    DOI: 10.1002/mana.70131
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