| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Nacl Rosario, CONICET, Lab Math Orsay, Rosario, Santa Fe - Argentina
[2] Univ Paris Sud, F-91405 Orsay - France
[3] Univ Paris Saclay, CNRS, Univ Paris Sud, Lab Math Orsay, F-91405 Orsay - France
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | JOURNAL OF GEOMETRIC ANALYSIS; v. 31, n. 1 NOV 2019. |
| Web of Science Citations: | 4 |
| 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, 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. (AU) | |
| FAPESP's process: | 15/23896-5 - Invariant structures on real flag manifolds |
| Grantee: | Viviana Jorgelina Del Barco |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |