Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2007; 44(1): 109-127

Printed January 1, 2007

Copyright © The Korean Mathematical Society.

Locally homogeneous critical metrics on four-dimensional manifolds

Yutae Kang

Sogang University

Abstract

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