A splitting theorem for Riemannian manifolds of generalised Ricci-Hessian type

Nicolas Ginoux (1) , Georges Habib (2) , Ines Kath (3)

1 IECL - Institut Élie Cartan de Lorraine
2 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]
3 HUB - Institut für Reine Mathematik

In this paper, we study and partially classify those Riemannian man-ifolds carrying a non-identically vanishing function f whose Hessian is minus f times the Ricci-tensor of the manifold.

Mots clés: Obata equation; Tashiro equation

Domaines: Géométrie différentielle [math.DG]

Nicolas Ginoux, Georges Habib, Ines Kath. A splitting theorem for Riemannian manifolds of generalised Ricci-Hessian type. 2018. ⟨hal-01877391⟩