Systolic Inequalities for Compact Quotients of Carnot Groups with Popp's Volume

Abstract

In this paper, we give a systolic inequality for quotient spaces of Carnot groups Γ\G with Popp's volume. Namely we show the existence of a positive constant C > 0 such that the systole of Γ\G is less than Cvol(Γ\G) 1 Q , where Q is the Hausdorff dimension. Moreover the constant depends only on the dimension of grading of the Lie algebra g = Vi.