R-critical Weyl structures

초록

Weyl structures can be. viewed as generalizations of Riemannian metrics.. We study Weyl structures Which are critical points of the squared L-2 norm functional of the full curvature tensor, defined on the space of Weyl structures on a compact 4-manifold. We find some relationship-between these critical Weyl structures and the critical Riemannian, metrics. Then in a search for homogeneous critical structures we study left-invariant.,metrics on some solv-manifolds and prove that they are not critical.

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