A Result of Rigidity for Ricci-Flat Warped Products

被引：0

作者：

Menezes, Ilton ^{[1
]}

Correia, Paula ^{[2
]}

Pina, Romildo ^{[2
]}

机构：

[1] Univ Fed Oeste Bahia, CCET, BR-47810047 Barreiras, BA, Brazil

[2] Univ Fed Goias, IME, BR-74690900 Goiania, GO, Brazil

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2023年 / 54卷 / 03期

关键词：

Ricci-flat warped product; Generalized Schwarzschild metric; Pseudo-orthogonal group;

D O I：

10.1007/s00574-023-00352-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work we prove a result of rigidity on Ricci-flat semi-Riemannian warped products when the base is locally conformally flat with scalar curvature zero and invariant by the action of the pseudo-orthogonal group. We obtain that in these manifolds the fiber must be 1-dimensional. As an application, every metric with these characteristics is a generalized Schwarzschild metric.

引用

页数：12

共 15 条

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