Characterization of contact structures for the dual form of the vector field of an h-Ricci-Bourguignon soliton on the product manifold D2 and R
Abstract
In this paper, we study h-Ricci-Bourguignon solitons on the product manifold D2 x R, where D2 is the Poincare disk equipped with its standard hyperbolic metric. We first establish that this manifold admits a gradient Ricci-Bourguignon h-soliton only if the non-zero function h depends solely on the manifold's last coordinate. Next, in the case where h:=1, we explicitly determine the vector field that makes D2 x R a Ricci-Bourguignon soliton. Finally, we provide the necessary and sufficient condition for the dual 1-form of this vector field to define a contact structure, which corresponds to the existence of an explicitly determined function independent of the manifold's second local coordinate, thereby allowing us to compute its Reeb vector field.
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BibTeX
@misc{diop2026characterization,
title = {{Characterization of contact structures for the dual form of the vector field of an h-Ricci-Bourguignon soliton on the product manifold D2 and R}},
author = {Mafal Ndiaye Diop and Abdou Bousso and Ameth Ndiaye},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14291},
eprint = {2609.14291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14291},
}
RIS
TY - UNPB
TI - Characterization of contact structures for the dual form of the vector field of an h-Ricci-Bourguignon soliton on the product manifold D2 and R
AU - Mafal Ndiaye Diop
AU - Abdou Bousso
AU - Ameth Ndiaye
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14291
UR - https://arxiv.org/abs/2609.14291
AB - In this paper, we study h-Ricci-Bourguignon solitons on the product manifold D2 x R, where D2 is the Poincare disk equipped with its standard hyperbolic metric. We first establish that this manifold admits a gradient Ricci-Bourguignon h-soliton only if the non-zero function h depends solely on the manifold's last coordinate. Next, in the case where h:=1, we explicitly determine the vector field that makes D2 x R a Ricci-Bourguignon soliton. Finally, we provide the necessary and sufficient condition for the dual 1-form of this vector field to define a contact structure, which corresponds to the existence of an explicitly determined function independent of the manifold's second local coordinate, thereby allowing us to compute its Reeb vector field.
ER -