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PreprintCC BY 4.0arXiv

An integral inequality for compact Bach-flat ๐’œ2-manifolds

  • Fรกbio Reis dos Santos
  • Elisa Joaquim Santos
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Abstract

We establish a Catino-type integral inequality for closed Bach-flat ๐’œ2-manifolds, namely Riemannian manifolds with nonnegative scalar curvature and constant nonnegative second Schouten curvature. In the equality case, we derive rigidity results showing that the manifold is either Einstein or isometrically covered by ๐•Š1ร—๐•Šnโˆ’1(ฮบ) endowed with the product metric.

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Cite

BibTeXRIS
BibTeX
@misc{santos2026integral,
  title = {{An integral inequality for compact Bach-flat $\mathcalA_2$-manifolds}},
  author = {Fรกbio Reis dos Santos and Elisa Joaquim Santos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.16552},
  eprint = {2607.16552},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.16552},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An integral inequality for compact Bach-flat ๐’œ_2-manifolds
AU  - Fรกbio Reis dos Santos
AU  - Elisa Joaquim Santos
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.16552
UR  - https://arxiv.org/abs/2607.16552
AB  - We establish a Catino-type integral inequality for closed Bach-flat ๐’œ_2-manifolds, namely Riemannian manifolds with nonnegative scalar curvature and constant nonnegative second Schouten curvature. In the equality case, we derive rigidity results showing that the manifold is either Einstein or isometrically covered by ๐•Š^1ร—๐•Š^nโˆ’1(ฮบ) endowed with the product metric.
ER  -