Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators

Simple item page
dc.creatorGilkey, P.
dc.creatorNikcevic, S.
dc.creatorWesterman, D.
dc.date2008-11-24
dc.date.accessioned2026-07-07T10:20:39Z
dc.date.available2026-07-07T10:20:39Z
dc.descriptionWe examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at a point P of a manifold M and suppose given a real analytic (resp. C-k for finite k at least 2) pseudo-Riemannian metric on M defined near P. We construct a torsion free real analytic (resp. C-k) connection D which is defined near P on the tangent bundle of M whose curvature operator is the given operator R at P and so that D has constant scalar curvature. We show that if R is Ricci symmetric, then D can be chosen to be Ricci symmetric; if R has trace free Ricci tensor, then D can be chosen to have trace free Ricci tensor; if R is Ricci alternating, then D can be chosen to be Ricci alternating.
dc.identifierhttps://arxiv.org/abs/0811.3841
dc.identifierhttp://arxiv.org/abs/0811.3841
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174917
dc.subjectDifferential Geometry
dc.subject53B20
dc.titleRiemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators
dc.typetext

Files

Collections

arXiv