Positive Ricci curvature on fiber bundles with compact structure group
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Leonardo Francisco Cavenaghi
and
Llohann Dallagnol Sperança
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.
Funding statement: The first named author was financially supported byCNPq 131875/2016-7 and by FAPESP 2017/24680-1. The second named author was financially supported by CNPq 404266/2016-9.
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Communicated by: T. Leistner
Acknowledgements
The authors are grateful to the anonymous referees for their relevant suggestions. The first author would like to thank Augusto Pereira, Gustavo Costa and Renato Júnior for the criticism and help. He also thanks Prof. Marcos Alexandrino, Prof. Francisco Caramello and Daniel Fadel for the encouragement and comments on earlier versions of this paper.
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Articles in the same Issue
- Frontmatter
- Ricci almost solitons with associated projective vector field
- Stein domains in ℂ2 with prescribed boundary
- Two examples of harmonic maps into spheres
- Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups
- The moduli space of tropical curves with fixed Newton polygon
- On nilpotent automorphism groups of function fields
- Locally homogeneous non-gradient quasi-Einstein 3-manifolds
- Positive Ricci curvature on fiber bundles with compact structure group
- Rank one sheaves over quaternion algebras on Enriques surfaces
- The complexity of orientable graph manifolds
- Representability of Chow groups of codimension three cycles
- Harmonic sections of vector bundles with spherically symmetric metrics
Articles in the same Issue
- Frontmatter
- Ricci almost solitons with associated projective vector field
- Stein domains in ℂ2 with prescribed boundary
- Two examples of harmonic maps into spheres
- Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups
- The moduli space of tropical curves with fixed Newton polygon
- On nilpotent automorphism groups of function fields
- Locally homogeneous non-gradient quasi-Einstein 3-manifolds
- Positive Ricci curvature on fiber bundles with compact structure group
- Rank one sheaves over quaternion algebras on Enriques surfaces
- The complexity of orientable graph manifolds
- Representability of Chow groups of codimension three cycles
- Harmonic sections of vector bundles with spherically symmetric metrics
