Killing Forms on 2-Step Nilmanifolds

Autor(es)

del Barco, Viviana ^{[1, 2]} ; Moroianu, Andrei ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRIC ANALYSIS; v. 31, n. 1 NOV 2019.
• Citações Web of Science: 4

Resumo

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)

• Processo FAPESP: 15/23896-5 - Estruturas invariantes em variedades bandeira reais.
• Beneficiário: Viviana Jorgelina Del Barco
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado