question 2 may have some error in placement of indices. If anyone finds the real mistake, mention that in attempting the questions and solve further according to the correction

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Q.1 Given the vector v: R² → R², v = {x² + x², x1x2}. Find it's covariant derivatives if x₁ and x2 are the plane polar coordinates. Q.2 Evaluate/expand the following Tr(wigouVu), where the quantity in parenthesis is a scalar/inner product. Also prove that V(wgV₁) ax(wgV) or Vx(w₂VP) = ax (w₂VP). = Q.1 Given the vector v: R² → R², v = {x² + x², x1x2}. Find it's covariant derivatives if x₁ and x2 are the plane polar coordinates. Q.2 Evaluate/expand the following Tr(wigouVu), where the quantity in parenthesis is a scalar/inner product. Also prove that V(wgV₁) ax(wgV) or Vx(w₂VP) = ax (w₂VP). =

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Geodesic equation for spherical polar Coordinates ... View the full answer