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

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SUMMARY

The discussion centers on the computation of tensor components within a manifold structure. The user seeks validation on their methodology for calculating nonzero components and the overall correctness of their tensor computation process. Feedback received indicates that the approach is acceptable, affirming the user's method and encouraging further inquiries.

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  • Understanding of tensor calculus
  • Familiarity with manifold theory
  • Knowledge of differential geometry
  • Experience with mathematical computation tools
NEXT STEPS
  • Study the properties of tensors in differential geometry
  • Explore computational techniques for tensor analysis
  • Learn about specific manifold structures and their implications
  • Investigate software tools for tensor computations, such as Mathematica or MATLAB
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Mathematicians, physicists, and students engaged in advanced studies of tensor analysis and manifold theory will benefit from this discussion.

Amateur659
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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!
 

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It looks fine.
 
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Awesome, thanks for the feedback.
 

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