Doctoral thesis (Dissertations and theses)
Immersions of surfaces into SL(2,C) and into the space of geodesics of Hyperbolic space
EL EMAM, Christian
2020
 

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Keywords :
Differential geometry; Holomorphic Riemannian manifolds; Submanifolds; Transition geometry; Para-Kahler manifolds
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
EL EMAM, Christian ;  Università degli Studi di Pavia > Dipartimento di Matematica "Felice Casorati"
Language :
English
Title :
Immersions of surfaces into SL(2,C) and into the space of geodesics of Hyperbolic space
Defense date :
December 2020
Number of pages :
210
Institution :
UNIPV - Università degli Studi di Pavia, Pavia, Italy
Degree :
Docteur en Mathématiques
Promotor :
Bonsante, Francesco
President :
Segatti, Antonio
Available on ORBilu :
since 22 January 2021

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