Autor(es)

del Barco, Viviana ; Moroianu, Andrei

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF MATHEMATICS; v. N/A, p. 26-pg., 2025-10-10.

Resumo

A locally conformally product (LCP) structure on a compact conformal manifold is a closed non-exact Weyl connection (i.e. a linear connection which is locally but not globally the Levi-Civita connection of Riemannian metrics in the conformal class), with reducible holonomy. A left-invariant LCP structure on a compact quotient Gamma\G of a simply connected Riemannian Lie group (G,g) with Lie algebra & gfr; can be characterized in terms of a closed one-form theta is an element of & gfr;& lowast; and a non-zero subspace & ufr; subset of & gfr; satisfying some algebraic conditions. We show that these conditions are equivalent to the fact that & gfr; is isomorphic to a semidirect product of a non-unimodular Lie algebra acting on an abelian one by a conformal representation. This extends to the general case results from Andrada et al. [1] holding for solvmanifolds. In addition, we construct explicit examples of compact LCP manifolds which are not solvmanifolds. (AU)

• Processo FAPESP: 23/15089-9 - Aspectos da geometria conforme e Riemanniana em grupos de Lie e seus quocientes compactos.
• Beneficiário: Viviana Jorgelina Del Barco
• Modalidade de apoio: Auxílio à Pesquisa - Regular