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

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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 ] = - R 2 } . Let B = B R ( 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 (
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