# differential geometry

Differential geometry is the study of geometry using calculus; it
has many applications in physics, especially in the general
theory of relativity. The objects studied by differential geometry are
known as **Riemannian manifolds** (see manifold).
These are geometrical objects, such as surfaces, that locally look like Euclidean space and therefore allow
the definition of analytical concepts such as tangent vectors and tangent space, differentiability,
and vector and tensor fields. Riemannian
manifolds have a metric, which opens the
door to measurement because it allows distances and angles to be evaluated
locally and concepts such as geodesics, curvature, and torsion to be defined.