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Improve support for semi-Riemannian manifolds #422

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mateuszbaran opened this issue Sep 8, 2021 · 3 comments
Open
6 tasks

Improve support for semi-Riemannian manifolds #422

mateuszbaran opened this issue Sep 8, 2021 · 3 comments

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@mateuszbaran
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Semi-Riemannian manifolds require different methods, see https://arxiv.org/abs/1812.07643 .

  • Finding ONBs,
  • indefinite orthogonal group,
  • pseudo-spheres,
  • pseudo-hyperbolic spaces,
  • semi-Riemannian geometry of SPD,
  • semi-Riemannian geometry of matrix Lie groups (?)
@kellertuer
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Should we introduce an interims type AbstractRiemannianManifold <: AbstractManifold and a AbstractSemiRiemannianManifold <: AbstractManifold to distinguish between manifolds that are Riemannian and those that are not? Might be too complicated since it depends on the metric and then the MetricManifold-Decorator might actually change that?

@mateuszbaran
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I'd prefer to have a trait instead of an abstract type like AbstractRiemannianManifold but there should definitely be a way to distinguish Riemannian and pseudo-Riemannian manifolds.

@kellertuer
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A trait sounds good, because that means we can “activate” it for different metric manifolds.

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