- #1
murmillo
- 118
- 0
I'm trying to understand parallel transport and I'm stuck. The example given is if you have a unit sphere and you take one of the latitudes (not the equator), take at a point on the latitude the tangent vector to the curve, and parallel transport it around the curve. I don't understand why the vector field rotates counterclockwise. According to the notes, "If we just take the covariant derivative of the tangent vector to the circle, it points upwards, so the vector field must rotate counterclockwise to counteract that effect in order to remain parallel." I don't understand that sentence. Is it supposed to be obvious that the covariant derivative of the tangent vector points upwards? And what does he mean by counteracting the effect? Any help would be appreciated--I've spent a long time trying to understand this.