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

Autor: Jean-Louis Clerc, Mads Aunskjær Bech, Bent Ørsted
Přispěvatelé: Clerc, Jean-Louis, Institut for Matematiske Fag (IMF), Aarhus University [Aarhus], Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Mathematics - Differential Geometry
Geodesic
geodesic triangle
General Mathematics
Mathematics::Number Theory
Mathematics::Classical Analysis and ODEs
Type (model theory)
Computer Science::Computational Geometry
01 natural sciences
Omega
Combinatorics
Mathematics::Algebraic Geometry
Kahler form
Computer Science::Discrete Mathematics
0103 physical sciences
FOS: Mathematics
Physics::Atomic Physics
0101 mathematics
[MATH]Mathematics [math]
ComputingMilieux_MISCELLANEOUS
Mathematics
Hermitian symmetric space
automorphy kernel
010308 nuclear & particles physics
010102 general mathematics
[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
Surface (topology)
Differential Geometry (math.DG)
Computational Theory and Mathematics
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]
compact Hermitian symmetric space
Statistics
Probability and Uncertainty
[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
2010 MSC : 32M15
53C55
57T15
Symplectic geometry
Zdroj: São Paulo Journal of Mathematical Sciences
São Paulo Journal of Mathematical Sciences, Springer, 2018, 12 (2), pp.174-195. ⟨10.1007/s40863-018-0099-7⟩
ISSN: 1982-6907
2316-9028
DOI: 10.1007/s40863-018-0099-7⟩
Popis: Let M be an irreducible Hermitian symmetric space of compact type, and let $$\omega $$ be its Kahler form. For a triplet $$(p_1,p_2,p_3)$$ of points in M we study conditions under which a geodesic triangle $$\mathcal T(p_1,p_2,p_3)$$ with vertices $$p_1,p_2,p_3$$ can be unambiguously defined. We consider the integral $$A(p_1,p_2,p_3)=\int _\Sigma \omega $$ , where $$\Sigma $$ is a surface filling the triangle $$\mathcal T(p_1,p_2,p_3)$$ and discuss the dependence of $$A(p_1,p_2,p_3)$$ on the surface $$\Sigma $$ . 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.
Databáze: OpenAIRE
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