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$\DeclareMathOperator\SL{SL}\DeclareMathOperator\PSL{PSL}$I studied the interpretation of Teichmuller space as a representation space for surface groups in $\PSL(2,\mathbb{R})$. Now I am planning to ...

Consider the space $W$ of smooth time-like curves in $\mathbb{R}^{n,1}$ with fixed ends. Given $\gamma\in W$, consider the space $T_\gamma$ of all smooth normal fields along $\gamma$; one may think ...

I am asked the question in MSE, but did not get an answer. I hope that this question is appropriate for MOF. I am interested in Hyperbolic Geometry and its significance in low dimensional geometry (...

In a previous question by me I asked about Berger spheres and their Lorentzian analogue, squashed $AdS_3$ along Hopf fibres. It was well answered (by https://mathoverflow.net/users/13268/ben-mckay) ...

I am looking some references on the existence and non-existence of (space-like) harmonic maps solving the Dirichlet into the de-Sitter space. More precisely: Let, for $n\geq 3$, $$dS^n=\{ u\in \...