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SINGULARITIES OF THE RICCI FLOW MICHAEL T. ANDERSON
 

Summary: SINGULARITIES OF THE RICCI FLOW
MICHAEL T. ANDERSON
Department of Mathematics
S.U.N.Y. at Stony Brook
Stony Brook, N.Y. 11794-3651
E-mail: anderson@math.sunysb.edu
Introduction.
Fix a closed n-dimensional manifold M , and let M be the space of Rie-
mannian metrics on M . Similar to the reasoning leading to the Einstein
equations in general relativity, there is basically a unique simple and nat-
ural vector eld on the space M . Namely, the tangent space T g M consists
of symmetric bilinear forms; besides multiples of the metric itself, the Ricci
curvature Ric g of g is the only symmetric form depending on at most the
2nd derivatives of the metric, and invariant under coordinate changes, i.e.
a (0; 2) tensor formed from the metric. Thus, consider
X g = Ric g + g;
where ,  are scalars. Setting  = 2, the corresponding equation for the
ow of X is
(1) d
dt g(t) = 2Ric g(t) + g(t):

  

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

 

Collections: Mathematics