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.