Rigid Two-Step Nilpotent Lie Groups Relative to Multicontact Structures

Abstract

-Let fX i ; Y k g denote a fixed basis of the Lie algebra n of a connected and simply connected nilpotent Lie group N of step two. Under a technical assumption on fX i ; Y k g, we prove that the Lie algebra w of vector fields V on N that satisfy [V ; X i ] l i X i is finite dimensional, a property that we refer to as rigidity. Our proof allows the explicit count of dim w.

Rigidity of Carnot groups relative to multicontact structures

“…In [9] it is shown that a large class of nonrigid examples exists. As for multicontact structures, the reader is referred to [3,4,6,8,13,14,16].…”