Locally Conformal Analysis of Non-Degenerate Odd Pairs
Abstract
We study the locally conformal geometry of cosymplectic and coorientable contact manifolds within a common algebraic framework based on a non-degenerate odd pair: a one-form and a two-form whose appropriate wedge product defines a nowhere-vanishing top-degree form on an odd-dimensional manifold. We consider conformally compatible local geometric and Hamiltonian data and encode their gluing through a closed Lee form and the Lichnerowicz-de Rham differential. For locally conformal cosymplectic geometry, we introduce an equal-weight formulation in which the defining forms carry the same conformal weight. This formulation allows compatible local Hamiltonian vector fields to glue directly into a global Hamiltonian vector field without additional rescaling, thereby preserving the local dynamics. For contact geometry, we develop a twisted odd-pair formulation in which the Lee form records the conformal gluing of local Hamiltonian data, while the global one-form remains an ordinary contact form. We illustrate these constructions through time-dependent mass dynamics in the cosymplectic setting and dissipative particle dynamics in the contact setting.
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BibTeX
@misc{atesli2026locally,
title = {{Locally Conformal Analysis of Non-Degenerate Odd Pairs}},
author = {Begüm Ateşli and Aybike Çatal-Özer and Oğul Esen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00982},
eprint = {2611.00982},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00982},
}
RIS
TY - UNPB
TI - Locally Conformal Analysis of Non-Degenerate Odd Pairs
AU - Begüm Ateşli
AU - Aybike Çatal-Özer
AU - Oğul Esen
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00982
UR - https://arxiv.org/abs/2611.00982
AB - We study the locally conformal geometry of cosymplectic and coorientable contact manifolds within a common algebraic framework based on a non-degenerate odd pair: a one-form and a two-form whose appropriate wedge product defines a nowhere-vanishing top-degree form on an odd-dimensional manifold. We consider conformally compatible local geometric and Hamiltonian data and encode their gluing through a closed Lee form and the Lichnerowicz-de Rham differential. For locally conformal cosymplectic geometry, we introduce an equal-weight formulation in which the defining forms carry the same conformal weight. This formulation allows compatible local Hamiltonian vector fields to glue directly into a global Hamiltonian vector field without additional rescaling, thereby preserving the local dynamics. For contact geometry, we develop a twisted odd-pair formulation in which the Lee form records the conformal gluing of local Hamiltonian data, while the global one-form remains an ordinary contact form. We illustrate these constructions through time-dependent mass dynamics in the cosymplectic setting and dissipative particle dynamics in the contact setting.
ER -