Question: Find the geodesic equations and geodesic for spherical polar coordinates? Show that every point of R3 is isotropic for the metric ds = (x)-2(dx1)2

Find the geodesic equations and geodesic for spherical polar coordinates? Show that every point of R3 is isotropic for the metric ds = (x)-2(dx1)2

+ (x1)-2(dx) + (x1)-(dx)2 Also find the Ricci tensor of mixed kind.

Find the geodesic equations and geodesic for spherical polar coordinates? Show that every point of R3 is isotropic for the metric ds = (x)-2(dx1)2 + (x1)-2(dx) + (x1)-(dx)2 Also find the Ricci tensor of mixed kind. Question 3: (a) Define the followings (15 Marks) (i) Invariant (ii) Tensor (iii) Riemannian curvature (iv) Affine Tensor (v) Arc length (vi) Cartesian Tensor (6) (b) Prove the second Bianchi's identity? (9)

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