On the Existence of Certain Metrics with Non Parallel Ricci Tensor

2001/06/29 by A. Raouf Chouikha, Chouikha, A. Raouf
Mathematics · Physics and Astronomy · #53C21 #53C25 #58G30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Point processes and geometric inequalities #math-ph #math.DG #math.MP #msc:53C21 #msc:53C25 #msc:58G30

paper · pdf · doi:10.48550/arxiv.math/0106263

9 pages

openalex publication_date 2001/06/29 · arxiv created 2001/10/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A. Derdzinki [D] gave examples of Riemannian metrics with harmonic curvature and non parallel Ricci tensor on some compact manifolds (M,g] . We examine their existence as well as their number wich naturally depends on the geometry of the manifolds.

Related

• Non Parallelism of Ricci tensor of Pseudo-cylindric Metrics
• Inversion of some curvature operators near a parallel Ricci metric II: Non-compact manifold with bounded geometry
• Hypersurfaces and Codazzi tensors
• Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics
• Some canonical metrics \em via Aubin's local deformations