Rigid Two-Step Nilpotent Lie Groups Relative to Multicontact Structures

Abstract

Let {Xi,Yk} denote a fixed basis of theLie algebra n of a connected and simply connected nilpotent Lie group N of step two. Under a technical assumption on{Xi,Yk}, we prove that the Lie algebra M of vector fields V on N that satisfy [V,Xi] = λi__Xiis finite dimensional, a property that we refer to as rigidity. Our proofallows the explicit count of dim M.