Calculate Killing Vectors in 3-D Euclidean Space

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SUMMARY

The discussion focuses on calculating Killing vectors in 3-D Euclidean space, specifically using the Killing equation: \(d_a V_b + d_b V_a = 0\). The solution provided by Ray D'Inverno identifies the Killing vectors as \((d_x, d_y, d_z)\). The participant seeks clarification on the calculation process for these vectors, indicating a need for a deeper understanding of the underlying mathematics.

PREREQUISITES
  • Understanding of differential geometry concepts
  • Familiarity with the Killing equation
  • Basic knowledge of vector calculus
  • Experience with 3-D Euclidean space
NEXT STEPS
  • Study the derivation of the Killing equation in differential geometry
  • Learn about the implications of Killing vectors in physics
  • Explore examples of Killing vectors in different geometries
  • Investigate the role of symmetries in general relativity
USEFUL FOR

Students of mathematics and physics, particularly those studying differential geometry and general relativity, will benefit from this discussion.

BrunoSantos
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Homework Statement



My problem is to calculate to calculate killing vectors in 3-D euclidean space(flat space).

Homework Equations



The relevante equations are killing equation : d_a*V_b+d_b*V_a=0

The Attempt at a Solution


I found the solution in Ray D'Inverno and that is (d_x,d_y,d_z) but I can't find how this is calculate.
I hope you can help me .
Thanks
 
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