I Question regarding actual computation of tensor at point (Self Study)

Amateur659
Messages
4
Reaction score
2
Hello all,

I am hoping to get some feedback on the manner in which I performed computations towards solving the following problem.

question.PNG


There are a couple specific points which I am not confident of:
1. Did I properly account for the manifold structure in my computation of the nonzero components?
2. Is the general process by which I compute each tensor component correct?
IMG_20220213_010056272.jpg


Finally, please let me know if I am making a mistake posting such questions here.

Thank you for your time and feedback!
 

Attachments

  • question.PNG
    question.PNG
    8.7 KB · Views: 203
Physics news on Phys.org
It looks fine.
 
Awesome, thanks for the feedback.
 

Thread 'Injective immersion and embedding'

Hello! There is a simple line in the textbook. If ##S## is a manifold, an injectively immersed submanifold ##M## of ##S## is embedded if and only if ##M## is locally closed in ##S##. Recall the definition. M is locally closed if for each point ##x\in M## there open ##U\subset S## such that ##M\cap U## is closed in ##U##. Embedding to injective immesion is simple. The opposite direction is hard. Suppose I have ##N## as source manifold and ##f:N\rightarrow S## is the injective...
View full post »

Similar threads

I A couple questions about the Riemann Tensor, definition and convention
Replies
2
Views
3K
I Understanding Kunneth Formula and Tensor Product in r-Forms
Replies
2
Views
2K
I How to calculate basis vectors from metric tensor (as a matrix)?
Replies
6
Views
418
Finding a Community: Self-Studying Physics and Chemistry
Replies
1
Views
412
A On the dependence of the curvature tensor on the metric
Replies
6
Views
3K
Studying When to check the solutions during self-study?
Replies
7
Views
3K
Resources for self-studying PDEs
Replies
15
Views
2K
Studying Critique My Self-Study Schedule (Signal Processing & RF Electronics)
Replies
8
Views
2K
Studying What Are the Best Steps for Self-Teaching Theoretical Physics?
Replies
14
Views
3K
I Get geodesics & parallel transport on 2D surfaces (discrete timestep)
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top