2021
del Barco, Viviana; Moroianu, Andrei
Conformal Killing forms on 2-step nilpotent Riemannian Lie groups Journal Article
Em: Forum Mathematicum, vol. 33, iss. 5, 2021.
Resumo | Links | BibTeX | Tags: Conformal Killing forms, Riemannian Lie groups
@article{nokey,
title = {Conformal Killing forms on 2-step nilpotent Riemannian Lie groups},
author = {Viviana del Barco and Andrei Moroianu},
url = {https://www.degruyter.com/document/doi/10.1515/forum-2021-0026/html},
doi = {https://doi.org/10.1515/forum-2021-0026},
year = {2021},
date = {2021-07-18},
journal = {Forum Mathematicum},
volume = {33},
issue = {5},
abstract = {We study left-invariant conformal Killing 2- or 3-forms on simply connected 2-step nilpotent Riemannian Lie groups. We show that if the center of the group is of dimension greater than or equal to 4, then every such form is automatically coclosed (i.e. it is a Killing form). In addition, we prove that the only Riemannian 2-step nilpotent Lie groups with center of dimension at most 3 and admitting left-invariant non-coclosed conformal Killing 2- and 3-forms are the following: The Heisenberg Lie groups and their trivial 1-dimensional extensions, endowed with any left-invariant metric, and the simply connected Lie group corresponding to the free 2-step nilpotent Lie algebra on 3 generators, with a particular 1-parameter family of metrics. The explicit description of the space of conformal Killing 2- and 3-forms is provided in each case.},
keywords = {Conformal Killing forms, Riemannian Lie groups},
pubstate = {published},
tppubtype = {article}
}
We study left-invariant conformal Killing 2- or 3-forms on simply connected 2-step nilpotent Riemannian Lie groups. We show that if the center of the group is of dimension greater than or equal to 4, then every such form is automatically coclosed (i.e. it is a Killing form). In addition, we prove that the only Riemannian 2-step nilpotent Lie groups with center of dimension at most 3 and admitting left-invariant non-coclosed conformal Killing 2- and 3-forms are the following: The Heisenberg Lie groups and their trivial 1-dimensional extensions, endowed with any left-invariant metric, and the simply connected Lie group corresponding to the free 2-step nilpotent Lie algebra on 3 generators, with a particular 1-parameter family of metrics. The explicit description of the space of conformal Killing 2- and 3-forms is provided in each case.