HW201 - Differential Geometry 2 Homework 01 1 Let V be a...

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Unformatted text preview: Differential Geometry 2 Homework 01 1. Let V be a finite-dimensional real vector space on which [•|•] is an inner product of type (− + ...+). Fix R > 0 and select a point a in one component H of the hyperboloid {z ∈ V : [z |z ] = −R2 }. Let B = BR (a⊥ ) be the ball of radius R in a⊥ and calculate explicitly the pullback of the canonical Riemannian metric h on H via the inverse F : B → H of stereographic projection from −a. 2. Let (•|•) be a (positive-definite) inner product on the finite-dimensional real vector space V of which S is the unit sphere. Fix a ∈ S and let ψ = ψa : S − {a} → a⊥ be stereographic projection from a. Choose n ∈ S and determine explicitly the image under ψ of the ‘equatorial hypersphere’ n⊥ ∩ (S − {a}). 1 ...
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This note was uploaded on 07/08/2011 for the course MTG 6256 taught by Professor Robinson during the Spring '09 term at University of Florida.

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