J. Korean Math. Soc. 2007; 44(1): 109-127
Printed January 1, 2007
Copyright © The Korean Mathematical Society.
Yutae Kang
Sogang University
We classify complete, locally homogeneous metrics wi\-th finite volume on four-dimensional manifolds which are critical points for the squared $L^2$-norm functionals of either the full Riemannian curvature tensor or the Weyl curvature tensor defined on the space of Riemannian metrics. % Indeed we prove that they are all Einstein symmetric spaces.
Keywords: locally homogeneous metric, critical metric, $L^2$-norm curvature functional
MSC numbers: 58E11, 53C21
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