Geodesic planes in hyperbolic 3-manifolds

• 成果类型: Article
• 署名作者: McMullen, Curtis T.; Mohammadi, Amir; Oh, Hee
• 署名单位: Harvard University; University of California System; University of California San Diego; Yale University; Korea Institute for Advanced Study (KIAS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0711-3
• 发表日期: 2017
• 页码: 425-461
• 关键词: locally symmetric-spaces; frame flow

摘要

This paper initiates the study of rigidity for immersed, totally geodesic planes in hyperbolic 3-manifolds M of infinite volume. In the case of an acylindrical 3-manifold whose convex core has totally geodesic boundary, we show that the closure of any immersed geodesic plane is a properly immersed submanifold of M. On the other hand, we show that rigidity fails for quasifuchsian manifolds.