HW204 - Differential Geometry 2 Homework 04 1 Let...

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Unformatted text preview: Differential Geometry 2 Homework 04 1. Let V, (•|•) be an inner product space and let f be the real-valued function on V defined by v ∈ V ⇒ f (v ) = 2/(1 + (v |v )). Let g0 be the standard Riemannian metric on V and let g = f 2 g0 be the conformal metric. Explicitly calculate the curvatures R, S, s, and K . 2. Let (M, g ) be a Riemannian manifold of dimension strictly greater than two. Assume that K (Π) has the same value for each plane Π ⊂ Tp M ; show that it is then independent of p ∈ M . [The differential Bianchi identity should be considered.] 1 ...
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