The moving frame method and invariant subspace under parametric group actions

Subject Areas : Differential geometry

Y. Alipour Fakhri ¹ (Department of Mathematics, Payame Noor University, Tehran, Iran)
Y. Azadi ² (Department of Mathematics, Payame Noor University, Tehran, Iran)

Received: 2021-07-22 Accepted : 2021-09-28 Published : 2021-09-01

Keywords: moving frame, Differential equation, First integral, group action, invariant subspace,

Abstract :

‎For a given subspace as a solution space of a linear ODE‎, ‎we define a special linear parametric group action and prolong it to the jet bundle‎. ‎We determine these group parameters by moving frame method and prove that these group parameters are the first integrals of the given ODE‎. ‎These first integrals are used to construct the general form of operators which preserve given subspace invariant‎.

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