Thursday, August 30, 2018

homework and exercises - How to calculate Riemann and Ricci tensors for a sphere?



Let's have the metric for a sphere: dl2=R2(dψ2+sin2(ψ)(dθ2+sin2(θ)dφ2)). I tried to calculate Riemann or Ricci tensor's components, but I got problems with it.


The Ricci curvature must be Rij=2R2gij. But when I use definition of Ricci tensor, I can't turn the expression into the expression for the metric tensor


Maybe, there are siome hints, which can help?




No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...