- #1
jag
- 14
- 5
- Homework Statement
- Derive the relationship between Ricci scalar and Gauss curvature in 2-surface R = 2K
- Relevant Equations
- Ricci scalar and Gauss curvature in 2-surface,
, where ; given the Ricci tensor and Ricci scalar .
Hi,
I'm self-learning some physics topics and came across an exercise to derive the relationship between Ricci scalar and Gauss curvature in 2-surface, , where ; given the Ricci tensor and Ricci scalar .
My attempt:
and , yielding . Then, , which will yield . I'm also not sure whether repeating the index labels in the metric is correct.
Please kindly let me know if my thought process is incorrect. Looking for any kind of help. Thank you.
I'm self-learning some physics topics and came across an exercise to derive the relationship between Ricci scalar and Gauss curvature in 2-surface,
My attempt:
. The left-hand side of the equation remains the same in the next steps. => using Ricci tensor definition
Please kindly let me know if my thought process is incorrect. Looking for any kind of help. Thank you.