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Exponential map - Lie theory | A Wisdom Archive on Exponential map - Lie theory | | Exponential map - Lie theory A selection of articles related to Exponential map - Lie theory | |
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Exponential map, Exponential map - Definition, Exponential map - Lie theory, Exponential map - Properties, Exponential map - Relationships, Exponential map - Riemannian geometry, Exponential function, Matrix exponential, List of exponential topics
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ARTICLES RELATED TO Exponential map - Lie theory | |
| | |  Exponential map - Lie theory: Encyclopedia II - Exponential map - RelationshipsThe two notions of the exponential map coincide in the case of Lie groups equipped with bi-invariant metrics (i.e. Riemannian metrics invariant under left and right translation). In this case the geodesics through the identity are precisely the one-parameter subgroups of G.
Take the example that gives the "honest" exponential map. Consider the positive real numbers R+, a Lie group under the usual multiplication. Then each tangent space is just R. On each copy of R at the point y, we introduce the modified inner product
<u,v>y< ...
See also:Exponential map, Exponential map - Lie theory, Exponential map - Definition, Exponential map - Properties, Exponential map - Riemannian geometry, Exponential map - Definition, Exponential map - Properties, Exponential map - Relationships Read more here: » Exponential map: Encyclopedia II - Exponential map - Relationships |
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