Abstract
We classify 3-dimensional compact Riemannian manifolds (M3, g) that admit a non-constant solution to the equation −Δfg +Hess f − f Ric = μ Ric +λg for some special constants (μ, λ), under the assumption that the manifold has cyclic parallel Ricci tensor. Namely, the structures that we study here are: positive static triples, critical metrics of the volume functional, and critical metrics of the total scalar curvature functional. We also classify n-dimensional critical metrics of the volume functional with non-positive scalar curvature and satisfying the cyclic parallel Ricci tensor condition.
Acknowledgements
The authors would like to thank Rondinelle Batista, Wilson Cunha, Manoel Vieira and Kelton Bezerra for helpful discussions about this subject. The first author was partially supported by PPP/FAPEPI/MCT/CNPq, Brazil, grant 007/2018.
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Communicated by: T. Leistner
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Articles in the same Issue
- Frontmatter
- On vector bundles over reducible curves with a node
- Inscribed rectangle coincidences
- 𝔽p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
- Tetrahedral cages for unit discs
- When is M0,n(ℙ1,1) a Mori dream space?
- Rank-one isometries of CAT(0) cube complexes and their centralisers
- Wall-crossing in genus-zero hybrid theory
- The curve Yn = Xℓ(Xm + 1) over finite fields II
- Uniqueness results for bodies of constant width in the hyperbolic plane
- A note on large Kakeya sets
- On static manifolds and related critical spaces with cyclic parallel Ricci tensor
- The motivic Igusa zeta function of a space monomial curve with a plane semigroup
- Real hypersurfaces of non-flat complex space forms with two generalized conditions on the Jacobi structure operator