Time and place: Thursday, May 13, 9:30-10:00, 202 Chernoff HallTitle: How to Describe Infinitesimally the Symmetric Product? (½
hour)Abstract: The notion of Lie bracket of vector fields is
well-understood in differential geometry. Infinitesimally speaking, this
bracket measures how far the flows of these two vector fields are from
commuting. However, there is no such infinitesimal description for the
symmetric product of vector fields. So far this product has been used to
describe the geodesic invariance of a distribution infinitesimally [1].
In this talk we describe the symmetric product infinitesimally by means of the parallel transport. These results are useful to determine the accessibility distribution not only restricted to the zero section of the tangent bundle, as described in [2].
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