Seminar talk, 7 May 2008: Difference between revisions
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We study the geometry of differential equations determined uniquely by their point symmetries. The action of the infinitesimal group of point symmetries foliates the jet space where the equation live. Equations which are uniquely determined by their point symmetries are of two types: they either coincide with a leaf of the part of the jet space where the action is regular or they coincide with the singular subset of the action. Many examples are provided, ranging from minimal submanifolds and geodesics to Monge-Ampère equations and some of their generalizations. | We study the geometry of differential equations determined uniquely by their point symmetries. The action of the infinitesimal group of point symmetries foliates the jet space where the equation live. Equations which are uniquely determined by their point symmetries are of two types: they either coincide with a leaf of the part of the jet space where the action is regular or they coincide with the singular subset of the action. Many examples are provided, ranging from minimal submanifolds and geodesics to Monge-Ampère equations and some of their generalizations. | ||
[[Category: Seminar|Seminar talk 7991-94-92]] | |||
[[Category: Seminar abstracts|Seminar talk 7991-94-92]] | |||
Latest revision as of 22:05, 17 September 2009
Speaker: Raffaele Vitolo
Title: On differential equations characterized by their Lie point symmetries
Abstract:
We study the geometry of differential equations determined uniquely by their point symmetries. The action of the infinitesimal group of point symmetries foliates the jet space where the equation live. Equations which are uniquely determined by their point symmetries are of two types: they either coincide with a leaf of the part of the jet space where the action is regular or they coincide with the singular subset of the action. Many examples are provided, ranging from minimal submanifolds and geodesics to Monge-Ampère equations and some of their generalizations.