1547845439-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_I__Chow_

5. PERELMAN'S FORMALISM IN POTENTIALLY INFINITE DIMENSIONS 431

f''Y <Y.(3 -_ 2 1 c-m)'YP({) g <Y.9(3p -m + {) (39Ci.p -m - {). p9Ci.(3 -m )

= 2 1 c-m)'Y0(8 9 <Y.9f3o -m + Uf39<Y.o £) -m - uo9Ci.f3 £) -m )

= r~f3(sn).

D

Therefore the components of the Ricci tensor Rpq of (1ic, _gml1iJ are
given by

and

(Note that Re (SN)<Y.(3 = ~}/9<Y.(3·) Thus, the scalar curvature R of the

hypersurface (7ic, gmJ1iJ, where gm= {if*_qm, is (denote gm~ ,qmJ 1 -LJ