Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups
Abstract
We study infinitesimally homogeneous affine manifolds with prescribed structure groups. First, for the real symplectic group Sp(2n,ℝ), we prove that the corresponding infinitesimally homogeneous structures are precisely flat torsion-free symplectic affine structures. Second, for U(n)×{1}, whose G-structures are equivalent to almost contact metric data, we classify the torsion-free characteristic tensors and obtain the general torsional case by invariant deformation. The admissible torsion and inner-torsion parameters are governed by a single algebraic relation, and the horizontal distribution is contact precisely when a certain combination of these parameters does not vanish. We also describe the compatible connections and relate the torsion-free branches to trans-Sasakian geometry.
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BibTeX
@misc{arango2026infinitesimmaly,
title = {{Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups}},
author = {Carlos Alberto Marín Arango and Alejandro Pinilla Barrera},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19568},
eprint = {2609.19568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19568},
}
RIS
TY - UNPB
TI - Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups
AU - Carlos Alberto Marín Arango
AU - Alejandro Pinilla Barrera
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.19568
UR - https://arxiv.org/abs/2609.19568
AB - We study infinitesimally homogeneous affine manifolds with prescribed structure groups. First, for the real symplectic group Sp(2n,ℝ), we prove that the corresponding infinitesimally homogeneous structures are precisely flat torsion-free symplectic affine structures. Second, for U(n)×{1}, whose G-structures are equivalent to almost contact metric data, we classify the torsion-free characteristic tensors and obtain the general torsional case by invariant deformation. The admissible torsion and inner-torsion parameters are governed by a single algebraic relation, and the horizontal distribution is contact precisely when a certain combination of these parameters does not vanish. We also describe the compatible connections and relate the torsion-free branches to trans-Sasakian geometry.
ER -