| Reference : Immersions of surfaces into SL(2,C) and into the space of geodesics of Hyperbolic space |
| Dissertations and theses : Doctoral thesis | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/45784 | |||
| Immersions of surfaces into SL(2,C) and into the space of geodesics of Hyperbolic space | |
| English | |
El Emam, Christian  [Università degli Studi di Pavia > Dipartimento di Matematica "Felice Casorati"] | |
| Dec-2020 | |
| University of Pavia, Pavia, Italy | |
| Docteur en Mathématiques | |
| 210 | |
| Bonsante, Francesco | |
| Segatti, Antonio | |
| [en] Differential geometry ; Holomorphic Riemannian manifolds ; Submanifolds ; Transition geometry ; Para-Kahler manifolds | |
| [en] This thesis mainly treats two developments of the classical theory of hypersurfaces inside pseudo-Riemannian space forms.
The former - a joint work with Francesco Bonsante - consists in the study of immersions of smooth manifolds into holomorphic Riemannian space forms of constant curvature -1 (including SL(2,C) with a multiple of its Killing form): this leads to a Gauss-Codazzi theorem, it suggests an approach to holomorphic transitioning of immersions into pseudo-Riemannian space forms, a trick to construct holomorphic maps into the PSL(2,C)-character variety, and leads to a restatement of Bers theorem. The latter - a joint work with Andrea Seppi - consists in the study of immersions of n-manifolds inside the space of geodesics of the hyperbolic (n+1)-space. We give a characterization, in terms of the para-Kahler structure of this space of geodesics, of the Riemannian immersions which turn out to be Gauss maps of equivariant immersions into the hyperbolic space. | |
| http://hdl.handle.net/10993/45784 |
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