Hyperbolic Riemann tensor

[hajg-ijk]

This small PR implements the Riemann tensor for the Hyperbolic manifold, analogous to the one on the Sphere.

I know I should probably open an issue about this, but since it's related: I was wondering whether it would make sense to implement a sectional_curvature method for the manifolds where a riemann_tensor is available.

I also added a new textbook reference for the formula and myself to the list of contributors.

[codecov]

Codecov Report

Merging #651 (6ae7cf0) into master (22dc01d) will decrease coverage by 0.02%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #651      +/-   ##
==========================================
- Coverage   99.22%   99.20%   -0.02%     
==========================================
  Files         106      106              
  Lines       10430    10433       +3     
==========================================
+ Hits        10349    10350       +1     
- Misses         81       83       +2     

Files Changed	Coverage Δ
src/manifolds/Hyperbolic.jl	100.00% <100.00%> (ø)

... and 1 file with indirect coverage changes

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[mateuszbaran]

Thanks, I think this is a good addition.

I know I should probably open an issue about this, but since it's related: I was wondering whether it would make sense to implement a sectional_curvature method for the manifolds where a riemann_tensor is available

What is computing sectional curvatures useful for? I'm generally trying to avoid adding functions that don't have a practical use. Note that most of MetricManifold stuff needs to be revisited so don't pay too much attention to it.

[hajg-ijk]

What is computing sectional curvatures useful for? I'm generally trying to avoid adding functions that don't have a practical use. Note that most of MetricManifold stuff needs to be revisited so don't pay too much attention to it.

Honestly, I only thought about it because I am using it in what I am doing at the moment, which is also the reason why I implemented the Riemann tensor for the hyperbolic space. I thought about it as just a utility function, much like some cost functions are exported by Manopt. However, I am not sure about all the possible use cases, and one might of course argue that it only takes a few lines to implement if needed.

[mateuszbaran]

OK, sure, if you find it useful then we can add it to Manifolds.jl 🙂

[kellertuer]

I think that is a useful function that could be added (in a new PR), but should then also be properly documented what the interface is and what it does.

edit: Oh I misread the title, this function is indeed nice and useful here :) Thanks for documenting it carefully and directly also adding tests

[kellertuer]

looks good to me (lgtm).

[hajg-ijk]

I still don't understand why codecov/project fails. It laments an indirect change in the circle group, but when you look at it, it has no relation whatsoever to my changes.

[kellertuer]

Nighlty is ok to fail and the rest looks good. all is fine.