Difference between revisions of "Geodesic for a linear connection"
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Revision as of 21:13, 6 January 2012
Definition
Given data
 A connected differential manifold with tangent bundle denoted by .
 A linear connection for .
Definition part
Consider a smooth curve . Consider the connection along induced by , and consider the transport along for that connection. Then, we say that is a geodesic for if, under that transport, the tangent vector at gets transported, at time , to the tangent vector at .