2020
del Barco, Viviana; Moroianu, Andrei
Higher degree Killing forms on 2-step nilmanifolds Journal Article
Em: Journal of Algebra, vol. 563, pp. 251-273, 2020.
Resumo | Links | BibTeX | Tags: Killing forms
@article{nokey,
title = {Higher degree Killing forms on 2-step nilmanifolds},
author = {Viviana del Barco and Andrei Moroianu},
url = {https://www.sciencedirect.com/science/article/abs/pii/S0021869320303768?via%3Dihub},
doi = {https://doi.org/10.1016/j.jalgebra.2020.07.020},
year = {2020},
date = {2020-08-13},
journal = {Journal of Algebra},
volume = {563},
pages = {251-273},
abstract = {We study left-invariant Killing forms of arbitrary degree on simply connected 2-step nilpotent Lie groups endowed with left-invariant Riemannian metrics, and classify them when the center of the group is at most two-dimensional.},
keywords = {Killing forms},
pubstate = {published},
tppubtype = {article}
}
We study left-invariant Killing forms of arbitrary degree on simply connected 2-step nilpotent Lie groups endowed with left-invariant Riemannian metrics, and classify them when the center of the group is at most two-dimensional.
2019
del Barco, Viviana; Moroianu, Andrei
Killing Forms on 2-Step Nilmanifolds Journal Article
Em: The Journal of Geometric Analysis, vol. 31, pp. 863–887, 2019.
Resumo | Links | BibTeX | Tags: 2-step nilpotent Lie groups, Killing forms, Naturally reductive homogeneous spaces
@article{nokey,
title = {Killing Forms on 2-Step Nilmanifolds},
author = {Viviana del Barco and Andrei Moroianu },
url = {https://link.springer.com/article/10.1007/s12220-019-00304-1},
doi = {https://doi.org/10.1007/s12220-019-00304-1},
year = {2019},
date = {2019-11-05},
journal = {The Journal of Geometric Analysis},
volume = {31},
pages = {863\textendash887},
abstract = {We study left-invariant Killing k-forms on simply connected 2-step nilpotent Lie groups endowed with a left-invariant Riemannian metric. For k=2,3, we show that every left-invariant Killing k-form is a sum of Killing forms on the factors of the de Rham decomposition. Moreover, on each irreducible factor, non-zero Killing 2-forms define (after some modification) a bi-invariant orthogonal complex structure and non-zero Killing 3-forms arise only if the Riemannian Lie group is naturally reductive when viewed as a homogeneous space under the action of its isometry group. In both cases, k=2 or k=3, we show that the space of left-invariant Killing k-forms of an irreducible Riemannian 2-step nilpotent Lie group is at most one-dimensional.},
keywords = {2-step nilpotent Lie groups, Killing forms, Naturally reductive homogeneous spaces},
pubstate = {published},
tppubtype = {article}
}
We study left-invariant Killing k-forms on simply connected 2-step nilpotent Lie groups endowed with a left-invariant Riemannian metric. For k=2,3, we show that every left-invariant Killing k-form is a sum of Killing forms on the factors of the de Rham decomposition. Moreover, on each irreducible factor, non-zero Killing 2-forms define (after some modification) a bi-invariant orthogonal complex structure and non-zero Killing 3-forms arise only if the Riemannian Lie group is naturally reductive when viewed as a homogeneous space under the action of its isometry group. In both cases, k=2 or k=3, we show that the space of left-invariant Killing k-forms of an irreducible Riemannian 2-step nilpotent Lie group is at most one-dimensional.