# Topology of curved space

[SOLVED] Topology of curved space

## Homework Statement

The distance between a point (r, theta) and a nearby point (r + dr, theta + d\theta) on a positively curved sphere is given by

$$ds^2 = dr^2 + R^2 \sin ^2 (r/R)d\theta ^2$$

NOTE: I mean that ds^2 = (ds^2). My question is - how do I use this formula? What is what - can you explain it to me?

HallsofIvy