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PreprintCC BY 4.0arXiv

On Hypersurfaces of Space Forms That Are Gradient Yamabe Solitons

  • Jahnabi Chakraborti
  • Anandateertha Mangasuli
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Abstract

This paper studies nontrivial Yamabe gradient solitons occurring as complete immersed hypersurfaces with constant scalar curvature in space forms (M̅n(C), g̅). For solitons with non-vanishing gradients, we establish a structural characterization of the soliton by analyzing a regular level set Σ of the soliton function. In particular, imposing a suitable condition on the traceless part of the second fundamental form, ΦΣM̅ of Σ as a submanifold of the space form, we prove that the soliton either decomposes as a Riemannian product of ℝ and a totally umbilical submanifold of the space form, or satisfies a sharp lower bound on supΣ|ΦΣM̅|. Furthermore, we show that the lower bound is attained if, and only if, the soliton is isometric to a Riemannian product of ℝ and a parallel submanifold of the space form.

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Cite

BibTeXRIS
BibTeX
@misc{chakraborti2026hypersurfaces,
  title = {{On Hypersurfaces of Space Forms That Are Gradient Yamabe Solitons}},
  author = {Jahnabi Chakraborti and Anandateertha Mangasuli},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29298},
  eprint = {2608.29298},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29298},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On Hypersurfaces of Space Forms That Are Gradient Yamabe Solitons
AU  - Jahnabi Chakraborti
AU  - Anandateertha Mangasuli
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29298
UR  - https://arxiv.org/abs/2608.29298
AB  - This paper studies nontrivial Yamabe gradient solitons occurring as complete immersed hypersurfaces with constant scalar curvature in space forms (M̅^n(C), g̅). For solitons with non-vanishing gradients, we establish a structural characterization of the soliton by analyzing a regular level set Σ of the soliton function. In particular, imposing a suitable condition on the traceless part of the second fundamental form, Φ^Σ_M̅ of Σ as a submanifold of the space form, we prove that the soliton either decomposes as a Riemannian product of ℝ and a totally umbilical submanifold of the space form, or satisfies a sharp lower bound on sup_Σ|Φ^Σ_M̅|. Furthermore, we show that the lower bound is attained if, and only if, the soliton is isometric to a Riemannian product of ℝ and a parallel submanifold of the space form.
ER  -