Parallel transport is a concept in mathematics and physics that describes how a vector or other geometric object can be moved along a curved path while keeping its orientation in relation to the surface it is moving on.
Intuition for parallel transport is important because it helps us understand how vectors change as they move along a curved path, which is crucial in many fields such as differential geometry, general relativity, and computer graphics.
Regular transport moves an object from one point to another in a straight line, while parallel transport moves an object along a curved path while maintaining its orientation in relation to the surface it is moving on.
Parallel transport has many applications in physics and engineering, such as understanding the motion of particles in a gravitational field, calculating the curvature of a surface, and creating smooth animations in computer graphics.
Developing intuition for parallel transport requires a solid understanding of vector calculus, differential geometry, and the concept of tangent spaces. It also helps to visualize and practice with different examples and scenarios to gain a deeper understanding of how parallel transport works.