论文标题
将表面浸入SL（2，c）中以及双曲空间的大地学空间
Immersions of surfaces into SL(2,C) and into the space of geodesics of Hyperbolic space
论文作者
论文摘要
本论文主要处理伪里曼尼亚人空间内部的传播理论的两个发展。 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全体形态图到PSL（2，c）的特征品种，并导致重新定理。 后者 - 与Andrea Seppi的联合作品 - 包括研究N -manifolds浸入双曲线（N+1）空间中的N -manifolds的浸入。我们从地球植物空间的帕拉萨基结构（riemannian浸入）中给出了一个特征，这些结构被证明是浸入双曲线空间的高斯层的高斯图。
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-Sasaki structure of this space of geodesics, of the Riemannian immersions which turn out to be Gauss maps of equivariant immersions into the hyperbolic space.
