A Review of the Index Method in Closed Geodesic Problem

• 作者: Sai LIU Wei WANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 85-96
• 页数: 12页
• 语种: 英文

摘要

In this paper we review and systematize the index method in closed geodesic problem.As we know,the closed geodesic problem on compact Riemannian or Finsler manifold is a famous problem,and has far from been resolved.In recent years,the Maslov-type index theory for symplectic path has been applied to studying the closed geodesic problem,and has induced a great number of results on the multiplicity and stability of closed geodesics.We will systematically introduce these progresses in this review.