The symplectic area of a geodesic triangle in a Hermitian symmetric space of compact type

Let M be an irreducible Hermitian symmetric space of compact type, and let ω be its Kähler form. For a triplet ( p 1 , p 2 , p 3 ) of points in M we study conditions under which a geodesic triangle T ( p 1 , p 2 , p 3 ) with vertices p 1 , p 2 , p 3 can be unambiguously defined. We consider the inte...

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Bibliographic Details
Published in:São Paulo Journal of Mathematical Sciences 2018-12, Vol.12 (2), p.174-195
Main Authors: Bech, Mads Aunskjær, Clerc, Jean-Louis, Ørsted, Bent
Format: Article
Language:English
Subjects:
Apexes
Complex Variables
Dependence
Differential Geometry
Mathematics
Mathematics and Statistics
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Summary:Let M be an irreducible Hermitian symmetric space of compact type, and let ω be its Kähler form. For a triplet ( p 1 , p 2 , p 3 ) of points in M we study conditions under which a geodesic triangle T ( p 1 , p 2 , p 3 ) with vertices p 1 , p 2 , p 3 can be unambiguously defined. We consider the integral A ( p 1 , p 2 , p 3 ) = ∫ Σ ω , where Σ is a surface filling the triangle T ( p 1 , p 2 , p 3 ) and discuss the dependence of A ( p 1 , p 2 , p 3 ) on the surface Σ . Under mild conditions on the three points, we prove an explicit formula for A ( p 1 , p 2 , p 3 ) analogous to the known formula for the symplectic area of a geodesic triangle in a non-compact Hermitian symmetric space.
ISSN:1982-6907
2316-9028
2306-9028
DOI:10.1007/s40863-018-0099-7