Typo or server down?Orodruin said:
Works for me.fresh_42 said:Typo or server down?
Strange. Even the ping doesn't work.PAllen said:Works for me.
Works for me too. Firewalled/blacklisted where you are for some reason?fresh_42 said:Strange. Even the ping doesn't work.
I don't want to distract from the topic, but shouldn't a ping work beneath the firewall, apart from the fact that it is unlikely.Ibix said:Works for me too. Firewalled/blacklisted where you are for some reason?
(finally, I figured out the password of PF...)Orodruin said:
Gaussian normal coordinates and Riemann normal coordinates are two different coordinate systems used in differential geometry to describe the curvature of a Riemannian manifold. They allow for a local description of the curvature at a given point on the manifold.
Gaussian normal coordinates can be viewed as a special case of Riemann normal coordinates, where the metric tensor at the chosen point is diagonal. In other words, Gaussian coordinates are a simplified version of Riemann coordinates, making them easier to work with in certain situations.
The main advantage of using these coordinate systems is that they allow for a more intuitive understanding of the curvature of a Riemannian manifold at a specific point. This can be useful in various fields of mathematics and physics, such as general relativity and differential geometry.
In Gaussian normal coordinates, the metric tensor can be computed by taking the Euclidean metric and adding small corrections based on the curvature of the manifold at the chosen point. In Riemann normal coordinates, the metric tensor is computed by taking the Euclidean metric and adding terms that depend on the first and second derivatives of the metric tensor at the chosen point.
Gaussian normal coordinates and Riemann normal coordinates are commonly used in the study of Riemannian manifolds, which have applications in various branches of mathematics and physics, including general relativity, differential geometry, and topology.