Equidistribution of Expanding Translates of Curves in Homogeneous Spaces with the Action of(SO(n,1))k

• 作者: Lei YANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 205-224
• 页数: 20页
• 语种: 英文

摘要

Let X=G/Γ be a homogeneous space with ambient group G containing the group H=(SO(n,1))k and x ∈ X be such that Hx is dense in X.Given an analytic curve φ:I=[a,b]→ H,we will show that if φ satisfies certain geometric condition,then for a typical diagonal subgroup A={a(t):t ∈ R}? H the translates{a(t)φ(I)x:t＞0}of the curve φ(I)x will tend to be equidistributed in X as t →+∞.The proof is based on Ratner's theorem and linearization technique.