On $\protect \mathrm{PSL}(2,\protect \mathbb{C})$ and on the space of geodesics of $\protect \mathbb{H}^3$ as holomorphic Riemannian manifolds

Emam, Christian El

doi:10.5802/tsg.361

PSL (2, ℂ)

and on the space of geodesics of

ℍ^{3}

as holomorphic Riemannian manifolds

Emam, Christian El ¹

¹ Dipartimento di Matematica Felice Casorati, Universita degli Studi di Pavia, Via Ferrata 5, 27100, Pavia, (Italy)

Séminaire de théorie spectrale et géométrie, Tome 35 (2017-2019), pp. 9-21.

Résumé

We discuss some geometric aspects of $PSL (2, ℂ)$ , $SL (2, ℂ)$ , and the space $𝔾$ of the geodesics of $ℍ^{3}$ equipped with some suitable structures of Riemannian holomorphic manifolds of constant sectional curvature. We also observe that $𝔾$ is a symmetric space for the group $PSL (2, ℂ)$ and use it to deduce some correlations between their holomorphic Riemannian metrics.

Publié le : 2021-04-21

DOI : 10.5802/tsg.361

Affiliations des auteurs :

Emam, Christian El ¹

¹ Dipartimento di Matematica Felice Casorati, Universita degli Studi di Pavia, Via Ferrata 5, 27100, Pavia, (Italy)

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     title = {On $\protect \mathrm{PSL}(2,\protect \mathbb{C})$ and on the space of geodesics of $\protect \mathbb{H}^3$ as holomorphic {Riemannian} manifolds},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {9--21},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {35},
     year = {2017-2019},
     doi = {10.5802/tsg.361},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/tsg.361/}
}

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Emam, Christian El. On $\protect \mathrm{PSL}(2,\protect \mathbb{C})$ and on the space of geodesics of $\protect \mathbb{H}^3$ as holomorphic Riemannian manifolds. Séminaire de théorie spectrale et géométrie, Tome 35 (2017-2019), pp. 9-21. doi : 10.5802/tsg.361. http://www.numdam.org/articles/10.5802/tsg.361/

Bibliographie
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