Geodesic
Upper half-plane in the Grassmanian $Gr(n;2n)$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 406-411.

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We investigate the complex geometry of a multidimensional generalization $\mathcal{D}(n)$ of the upper-half-plane, which is homogeneous relative the group $G=SL(2n; \mathbb{R})$. For $n>1$ it is the pseudo Hermitian symmetric space which is the open orbit of $G=SL(2n; \mathbb{R})$ on the Grassmanian $Gr_\mathbb{C}(n;2n)$ of $n$-dimensional subspaces of $\mathbb{C}^{2n}$. The basic element of the construction is a canonical covering of $\mathcal{D}(n)$ by maximal Stein submanifolds — horospherical tubes.
Keywords: Grassmanian, pseudo Hermitian symmetric space, cycle, horosphere, horospherical tube. 
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Simon Gindikin. Upper half-plane in the Grassmanian $Gr(n;2n)$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 406-411. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a0/

[1] J.E. D'Atri, S.G. Gindikin, “Siegel domain realization of pseudo-Hermitian symmetric manifolds”, Geom. Dedicata, 46 (1993), 91–125 | DOI | MR | Zbl

[2] S.G. Gindikin, J. Faraut, “Pseudo-Hermitian symmetric spaces of tube type”, Progr. Nonlinear Differential Equations Appl., Topics in geometry, 20, 1996, 123–154 | MR | Zbl

[3] D.N. Akhiezer, S.G. Gindikin, “On Stein extensions of real symmetric spaces”, Math. Ann., 286 (1990), 1–12 | DOI | MR | Zbl

[4] S.G. Gindikin, T. Matsuki, “Stein extensions of Riemann symmetric spaces and dualities of orbits on flag manifolds”, Transformation Groups, 8:2003, 333–376 | MR | Zbl

[5] S.G. Gindikin, “Fourier transform and Hardy spaces of $\bar{\partial}$-cohomology in tube domains”, C. R. Acad. Sci. Paris, Ser. I Math., 315 (1992), 1139–1143 | MR | Zbl

[6] S.G. Gindikin, “Holomorphic language for $\bar{\partial}$-cohomology and representations of real semisimple Lie groups”, The Penrose Transform and Analytic Cohomology in Representation Theory, Cont. Math., 154, eds. M. Eastwood, J. Wolf, R. Zierau, Amer. Math. Soc., 1993, 103–115 | DOI | MR | Zbl

[7] T. Bailey, M. Eastwood, S.G. Gindikin, “Smoothly parameterized C̆ech cohomology of complex manifolds”, J. Geom. Anal., 15 (2005), 9–23 | DOI | MR | Zbl