Rotations in differential geometry

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Rotations in differential geometry involve mapping points in Euclidean space while preserving distances and the origin. The rotation matrix is defined as an invertible linear mapping, characterized by properties such as the transpose being equal to the inverse and a positive determinant. The angle between two geodesics at a point can be determined by the angle between their tangent vectors, which are elements of the tangent space at that point. For curves defined in terms of latitude and longitude on a sphere, the transformation between unrotated and rotated systems can be described using conformal maps, provided the transformation is a pure rotation. Understanding these concepts is crucial for applications in differential geodesy and curvature analysis.
  • #31
meteo student said:
Very nice. Learned something new. Pushforward and pullback.

I will calculate the Jacobian using the transformation functions and attempt to reproduce the published expressions.
Good luck, sorry I could not give you something more direct/clear.
 

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