## S=a*Ric iff the metric has constant curvaturre [closed]

Suppose (M,g) is immersed as a hypersurface in n-dimensional space,How to show that the shape Operator S=a*Ric iff the metric has constant curvaturre(a is a constant number)?

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This is a standard calculation using the definitions involved. Looks like homework. – Spiro Karigiannis Jan 4 2011 at 3:11