Hello! I read a derivation for the geodesic deviation: you have 2 nearby geodesics and define a vector connecting points of equal proper time and calculate the second covariant derivative of this vector. I understand the derivation but I am a bit confused about the actual definition of this connecting vector. Let's say we have point A on the first geodesic and B on the second. Is the vector somehow in the tangent space of A? And if so how do you define it as "going to B" as in a general curved manifold, B will obviously not lie in the tangent plane of A. Or is it some sort of curved vector (not sure if this even exists) i.e. you take a straight vector and paste it on the surface of the manifold letting it taking the shape of the path between A and B (but I guess it is not trivial to define such a path). Or it is just assumed that the points are so close that A and B actually lie in the same (Euclidean) plane and the vector connecting them is a normal, Euclidean vector? Thank you!