Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori
By D. Ferus, K. Leschke, F. Pedit, Ulrich Pinkall. 2000
103 citations recorded by the source corpus.
The paper develops the fundamentals of quaternionic holomorphic curve theory. The holomorphic functions in this theory are conformal maps from a Riemann surface into the 4-sphere, i.e., the quaternionic projective line. Basic results such as the Riemann-Roch Theorem for quaternionic holomorphic vector bundles, the Kodaira embedding and the Pluecker relations for linear systems are proven. Interpretations of these results in terms of the differential geometry of surfaces in 3- and 4-space are hinted at throughout the paper. Applications to estimates of the Willmore functional on constant mean curvature tori, respectively energy estimates of harmonic 2-tori, and to Dirac eigenvalue estimates on Riemannian spin bundles in dimension 2 are given.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/901d7763fabe589674392bd5c8a7690a0354cc1c
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Constrained Willmore tori in the 4-sphere (2008, methodology): “In the early nineties this prototype result had been generalized to harmonic maps from T 2 into various other symmetric target spaces [19, 12, 6] which led to the conjecture that Willmore tori as well should be of finite type, because they are characterized by the harmonicity of their conformal…”
- The geometric complexity of special Lagrangian T2-cones (2003, background): “We explain some consequences of our results for the programme (due to Joyce) to understand the “most common” three-dimensional isolated singularities of generic families of SLG submanifolds in almost Calabi-Yau manifolds.”