Compact pseudo-Riemannian manifolds with parallel Weyl tensor

被引：15

作者：

Derdzinski, Andrzej ^{[1
]}

Roter, Witold ^{[2
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2010年 / 37卷 / 01期

关键词：

Parallel Weyl tensor; Conformally symmetric manifold/metric; Compact pseudo-Riemannian manifold; CONFORMALLY SYMMETRIC MANIFOLDS; AFFINE; SPACES;

D O I：

10.1007/s10455-009-9173-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that in every dimension n = 3j + 2, j = 1, 2, 3, . . ., there exist compact pseudo-Riemannian manifolds with parallel Weyl tensor, which are Ricci-recurrent, but neither conformally flat nor locally symmetric, and represent all indefinite metric signatures. The manifolds in question are diffeomorphic to nontrivial torus bundles over the circle. They all arise from a construction that a priori yields bundles over the circle, having as the fibre either a torus, or a 2-step nilmanifold with a complete flat torsionfree connection; our argument only realizes the torus case.

引用

页码：73 / 90

页数：18

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