Weyl-parallel Forms and conformal Products

Florin Belgun (1) , Andrei Moroianu (2)

1 Institut für Mathematik [Berlin]
2 CMLS - Centre de Mathématiques Laurent Schwartz

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to describe in further detail the holonomy of the adapted Weyl connection on conformal products.

Mots clés: Conformal products; conformally parallel forms; Weyl structures; reducible holonomy

Domaines: Géométrie différentielle [math.DG]

Florin Belgun, Andrei Moroianu. Weyl-parallel Forms and conformal Products. 2009. ⟨hal-00355584⟩