 
Summary: EXTREMA OF CURVATURE FUNCTIONALS ON THE SPACE OF METRICS
ON 3MANIFOLDS, II.
MICHAEL T. ANDERSON
0. Introduction
This paper is a continuation of the study of some rigidity or nonexistence issues discussed in
[An1, x6]. The results obtained here also play a signicant role in the approach to geometrization of
3manifolds discussed in [An4].
Let N be an oriented 3manifold and consider the functional
R 2 (g) =
Z
N
jr g j 2 dV g ; (0.1)
on the space of metrics M on N where r is the Ricci curvature and dV is the volume form. The
EulerLagrange equations for a critical point of R 2 read
rR 2 = D Dr +D 2 s 2 Æ
R Ær 1
2
(s jrj 2 ) g = 0; (0.2)
s = 1
3
