Positive Ricci curvature on fiber bundles with compact structure group-Reference-Cited by-同舟云学术

Positive Ricci curvature on fiber bundles with compact structure group

Published:2022-01-01 Issue:1 Volume:22 Page:95-104
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Cavenaghi Leonardo Francisco¹,Sperança Llohann Dallagnol²

Affiliation:

1. Instituto de Matemática e Estatística – USP, R. do Matão, Vila Universitária , 1010, 05508-090 , São Paulo – SP , Brazil

2. Instituto de Ciência e Tecnologia – Unifesp, Avenida Cesare Mansueto Giulio Lattes , 1201, 12247-014 , São José dos Campos, SP , Brazil

Abstract

Abstract This paper presents a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact structure groups. In particular, it generalizes and puts in a unified framework the results of Nash [12] and Poor [15]. With the intention of disseminating this result,we apply it to build new examples of manifolds with positive Ricci curvature, including bundles whose base consists of gradient shrinking Ricci solitons.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2021-0007/pdf

Reference22 articles.

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3. L. F. Cavenaghi, L. D. Sperança, On the Geometry of Some Equivariantly Related Manifolds. Int. Math. Res. Not. no. 23 (2020), 9730–9768. MR4182809 Zbl 1464.53044

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