This involves the study of manifolds that are equipped with the additional structure of a Riemannian metric, a rule for measuring curve lengths and angles between tangent vectors. A Riemannian manifold has curvature, and it is specifically this curvature that makes up the laws of classical Euclidean...
To draw the graph, plot all points corresponding to x-intercepts, minima, maxima with one cycle. Draw the level curves of the function f(x, y) = x^2 +2x - y^2, and use them to draw a rough graph of the surface z = f(x,y). Funct...