On the two-systole of real projective spaces. (English) Zbl 1462.53005
The authors establish an integral-geometric formula for minimal two-spheres inside homogeneous three-spheres, and use it to provide a characterisation of each homogeneous metric on the three-dimensional real projective space as the unique metric with the largest possible two-systole among metrics with the same volume in its conformal class. Reference [12] should be corrected to [W. H. Meeks III et al., Invent. Math. 224, No. 1, 147–244 (2021; Zbl 1527.53051)].
Reviewer: Andreas Arvanitoyeorgos (Patras)
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53A20 | Projective differential geometry |
| 53C30 | Differential geometry of homogeneous manifolds |
Citations:
Zbl 1527.53051References:
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