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EXTREMA OF CURVATURE FUNCTIONALS ON THE SPACE OF METRICS ON 3-MANIFOLDS, II.
 

Summary: EXTREMA OF CURVATURE FUNCTIONALS ON THE SPACE OF METRICS
ON 3-MANIFOLDS, II.
MICHAEL T. ANDERSON
0. Introduction
This paper is a continuation of the study of some rigidity or non-existence issues discussed in
[An1, x6]. The results obtained here also play a signi cant role in the approach to geometrization of
3-manifolds discussed in [An4].
Let N be an oriented 3-manifold 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
Euler-Lagrange equations for a critical point of R 2 read
rR 2 = D  Dr +D 2 s 2
R r 1
2
(s jrj 2 )  g = 0; (0.2)
s = 1
3

  

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics