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PreprintCC BY 4.0arXiv

Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length

  • Hemangi Madhusudan Shah
  • Sharief Deshmukh
  • Mohammad Aqib
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Abstract

We study non-compact Ricci solitons of finite volume whose potential vector field has constant length. Under the assumptions that the scalar curvature is constant along the integral curves of the potential field and that a natural divergence term is integrable on the unit tangent bundle, we prove that such Ricci solitons are necessarily trivial. As applications, we characterise $3$-dimensional Ricci solitons of constant length and of finite volume on almost α-cosymplectic manifolds. In fact, we show that these spaces are indeed compact quotients of Euclidean spaces. We also study complete, non-compact and finite volume contact metric manifolds in dimension $3$ admitting a Reeb vector field as a Ricci soliton. We show that it is a compact spherical space form. We include some examples to illustrate the necessity of the finite-volume and constant-length assumptions.

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Cite

BibTeXRIS
BibTeX
@misc{shah2026noncompact,
  title = {{Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length}},
  author = {Hemangi Madhusudan Shah and Sharief Deshmukh and Mohammad Aqib},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.22394},
  eprint = {2607.22394},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22394},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length
AU  - Hemangi Madhusudan Shah
AU  - Sharief Deshmukh
AU  - Mohammad Aqib
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2607.22394
UR  - https://arxiv.org/abs/2607.22394
AB  - We study non-compact Ricci solitons of finite volume whose potential vector field has constant length. Under the assumptions that the scalar curvature is constant along the integral curves of the potential field and that a natural divergence term is integrable on the unit tangent bundle, we prove that such Ricci solitons are necessarily trivial. As applications, we characterise $3$-dimensional Ricci solitons of constant length and of finite volume on almost α-cosymplectic manifolds. In fact, we show that these spaces are indeed compact quotients of Euclidean spaces. We also study complete, non-compact and finite volume contact metric manifolds in dimension $3$ admitting a Reeb vector field as a Ricci soliton. We show that it is a compact spherical space form. We include some examples to illustrate the necessity of the finite-volume and constant-length assumptions.
ER  -