Geodesics on the extended Siegel-Jacobi upper half-plane

2021/01/20 by Stefan Berceanu, Berceanu, Stefan
Mathematics · #32F45 #53C22 #53C30 #53C55 #81R30 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2101.08015

openalex publication_date 2021/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The semidirect product of the real Heisenberg group \rm H₁(ℝ) with \rm SL(2,ℝ), called the real Jacobi group G^J₁(ℝ), admits a four-parameter invariant metric expressed in the S-coordinates. We determine the geodesic equations on the extended Siegel--Jacobi upper half-plane X^J₁ =\fracG^J₁(\R)\rmSO(2)\approxX^J₁×ℝ≈ X₁ ×ℝ³, where X^J₁ (X₁) denotes the Siegel-Jacobi upper half-plane (respectively Siegel upper half-plane). Equating successively with zero the values of the three parameters in the geodesic equations on X^J₁, we get the geodesic equations on X^J₁, X₁ and \rm H₁(ℝ).

Citations

• Geodesics associated to the balanced metric on the Siegel-Jacobi ball

Related

• Remarks on the geometry of the extended Siegel--Jacobi upper half-plane
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• Classification of the geodesic curves of the sub-Riemannian LR system on the Heisenberg group in dimension 5
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