Evolution of the Weyl Tensor under the Ricci Flow

Abstract

We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.

References in corpus (3)

• Conformal de Rham decomposition of Riemannian manifolds
• On Locally Conformally Flat Gradient Shrinking Ricci Solitons
• On Locally Conformally Flat Gradient Steady Ricci Solitons

Cited by in corpus (22)

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• The Weyl Tensor of Gradient Ricci Solitons
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• On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor
• Curvature Estimates for Four-Dimensional Gradient Steady Ricci Solitons
• The Curvature of Gradient Ricci Solitons
• On the injectivity radius and tangent cones at infinity of gradient Ricci solitons
• Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature
• On Locally Conformally Flat Gradient Steady Ricci Solitons
• On rigidity of gradient Kähler-Ricci solitons with harmonic Bochner tensor
• Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equations
• Berger curvature decomposition, Weitzenböck formula, and canonical metrics on four-manifolds
• Cohomogeneity two Ricci solitons with sub-Euclidean volume
• Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature
• Towards an Entropic Geometrodynamics of Quantum Particles: Mouths of Casimir Wormholes as Planckeons
• Isoperimetric inequality and Weitzenböck type formula for critical metrics of the volume
• Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons
• Generalized Ricci flow II: existence for noncompact complete manifolds
• The Cotton tensor and the Ricci flow