
The exponential map on the hyperbolic space

The exponential map on the hyperbolic space $\mathbb H^n$ is given for $x\in\mathbb H^n$ and $\xi\in T_x{\mathbb H^n}$ by the formula

where $\langle\cdot,\cdot\rangle_M$ denotes the Minkowski metric.

Matlab Documentation

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% exp(x,xi) exponential map at the point(s) x towards xi in T_xHn
%
% INPUT
%   x : a point or set of points on the manifold Hn
%  xi : a point or set of point in the tangential spaces TxHn
%
% OPTIONAL
%   t : shorten vectors xi by factor t
%   (given as one value or an array of same length as number of xis)
%
% OUTPUT
%   y : resulting point(s) on Hn
% ---
% Manifold-Valued Image Restoration Toolbox 1.
%  R. Bergmann ~ 2015-01-20 | 2015-10-20