η-Invariant and a problem of Berard-Bergery on the existence of closed geodesics

被引：5

作者：

Tang, Zizhou ^{[1
]}

Zhang, Weiping ^{[2
,3
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2014年 / 254卷

关键词：

Eells-Kuiper projective plane; SCp structure; mu invariant; eta invariant; DIFFEOMORPHISM CLASSIFICATION; MANIFOLDS;

D O I：

10.1016/j.aim.2013.12.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use the eta-invariant of Atiyah Patodi Singer to compute the Eells Kuiper invariant for the Eells Kuiper quaternionic projective plane. By combining with a known result of Berard-Bergery, it shows that every Eells Kuiper quaternionic projective plane carries a Riemannian metric such that all geodesics passing through a certain point are simply closed and of the same length. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：41 / 48

页数：8

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