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Rigidity of projective area widths and a weighted Crofton formula on RP3

  • Tongrui Wang
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Abstract

We show that a Riemannian metric on RP3 is a surface Zoll metric if and only if its four projective area widths are equal. We also establish a weighted Crofton formula on RP3 under surface Zoll metrics, from which we derive an inequality relating the systole, the volume, and the common value of the projective area widths.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026rigidity,
  title = {{Rigidity of projective area widths and a weighted Crofton formula on $RP^3$}},
  author = {Tongrui Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28310},
  eprint = {2609.28310},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28310},
}
RIS
TY  - UNPB
TI  - Rigidity of projective area widths and a weighted Crofton formula on RP^3
AU  - Tongrui Wang
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28310
UR  - https://arxiv.org/abs/2609.28310
AB  - We show that a Riemannian metric on RP^3 is a surface Zoll metric if and only if its four projective area widths are equal. We also establish a weighted Crofton formula on RP^3 under surface Zoll metrics, from which we derive an inequality relating the systole, the volume, and the common value of the projective area widths.
ER  -