Lecture 10: Metric Manifolds (International Winter School on Gravity and Light 2015)

[@ErnestYAlumni]

This lecture is PACKED with a lot of GOOD stuff, explaining lucidly, explicitly, clearly, a lot of the tools needed in GR (and a lot of other places): Levi Civita connection, Ricci scalar, Ricci curvature, Riemann-christoffel curvature. This is truly a service, because a lot of other presentations are confusing.

[@paoloziko]

+ErnestYAlumni can You answer my last post ? because I got confused when he explained the musical map and so on, I couldn't grasp that notion of non degeneracy... degeneracy of what?

[@ErnestYAlumni]

I just checked this comment (you can also try to email or tweet me; etc. I don't check my KZbin very often). degeneracy of the metric, so essentially, if a metric is nondegenerate then (x,y)=0 and x != 0 (x is not zero) then y MUST BE zero. cf. en.wikipedia.org/wiki/Pseudo-Riemannian_manifold

[@truebomba]

Can you pleas point me in what lecture I can find explanation of the Tensor notation and the the tensor field function transformation low referred to in 21: 38

[@paoloziko]

Hi , good lectures for sure. I'm still confused with the property of non degeneracy. Is it the inversibility of g or something else? please correct me if I'm mistaken. ty