Changes between Version 3 and Version 9 of Ticket #24622
- Timestamp:
- 02/07/18 19:50:07 (3 years ago)
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Ticket #24622
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Ticket #24622 – Description
v3 v9 1 This ticket implements pseudo-Riemannian manifolds, i.e. real differentiable manifolds equipped with a metric tensor. Important subcases are of course Riemannian manifolds and Lorentzian manifolds. Taking into account that genericmetric tensors are already implemented in Sage (see [http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/metric.html here]), this ticket introduces1 This ticket implements pseudo-Riemannian manifolds, i.e. real differentiable manifolds equipped with a metric tensor. Important subcases are of course Riemannian manifolds and Lorentzian manifolds. Taking into account that pseudo-Riemannian metric tensors are already implemented in Sage (see [http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/metric.html here]), this ticket introduces 2 2 3 - the parent class `PseudoRiemannianManifold`, as a subclass of the existing class `DifferentiableManifold` 4 - new methods `gradient` and `laplacian` for scalar fields5 - new methods `divergence`, `laplacian` for tensor fields6 - new methods `curl`, `dot _product`, `cross_product` and `norm` for vector fields3 - the parent class `PseudoRiemannianManifold`, as a subclass of the existing class `DifferentiableManifold`, with the specific methods `metric` and `volume_form` 4 - new methods `gradient`, `laplacian` and `dalembertian` for scalar fields 5 - new methods `divergence`, `laplacian` and `dalembertian` for tensor fields 6 - new methods `curl`, `dot`, `cross` and `norm` for vector fields 7 7 8 8 For a greater generality, all these methods have an optional argument `metric`; if it is omitted, the metric of the underlying pseudo-Riemannian manifold is assumed. The follow-up ticket #24623 implements Euclidean spaces.