On a Harmonic Property of the Einstein Manifold Curvature

1995/03/24 by O. V. Babourova, Babourova, O. V., B. N. Frolov +1
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc

paper · pdf · doi:10.48550/arxiv.gr-qc/9503045

4 pages

arxiv created 1995/03/24 · arxiv updated 2009/11/30

Abstract

The harmonicity condition of the curvature 2-form of a pseudo- Riemannian manifold is formulated on the basis of annulment of this form by the de Rham-Lichnerowicz Laplacian. The following theorem is proved: The curvature 2-form of any Einstein manifold is harmonic.

Related

• Harmonic morphisms with one-dimensional fibres on Einstein manifolds
• Curvature conditions for complex-valued harmonic morphisms
• Double forms, curvature structures and the (p,q)-curvatures
• Liouville Type Theorem about p-harmonic 1 form, p-harmonic map and harmonic q form
• The two-jet of the curvature tensor of an Einstein manifold