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Quartic differentials and harmonic maps in conformal surface geometry
- Source :
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :1507-1524
- Publication Year :
- 2022
- Publisher :
- Scuola Normale Superiore - Edizioni della Normale, 2022.
-
Abstract
- We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. We characterise the orthogonal surfaces of such congruences as either $S$-Willmore surfaces, quasi-umbilical surfaces, constant mean curvature surfaces in 3-dimensional space forms or surfaces of constant lightlike mean curvature in 3-dimensional lightcones. We then investigate Bryant's quartic differential in this context and show that generically this is divergence free if and only if the surface under consideration is either superconformal or orthogonal to a harmonic congruence of codimension 2 spheres. We may then apply the previous result to characterise surfaces with such a property.<br />15 pages
- Subjects :
- Holomorphic differentials
Mathematics - Differential Geometry
Surface (mathematics)
Physics
53A31, 53B25, 53C43
Mean curvature
Mathematical analysis
Harmonic map
Conformal map
Harmonic (mathematics)
Codimension
Conformal Geometry
Theoretical Computer Science
Mathematics (miscellaneous)
Differential Geometry (math.DG)
Quartic function
Harmonic Maps
FOS: Mathematics
Congruence (manifolds)
Mathematics::Differential Geometry
Harmonic Maps, Holomorphic differentials, Conformal Geometry
Subjects
Details
- ISSN :
- 20362145 and 0391173X
- Database :
- OpenAIRE
- Journal :
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- Accession number :
- edsair.doi.dedup.....9593f4bd0bedb27e5f5d26616e0f660f