Jacobi field

Definition

A vector field $V$ along a curve $\gamma :[0,1]\to M$ is termed a Jacobi field if it satisfies the following equation, where $T$ is the tangent field for the curve and $D$ denotes covariant derivative:

$D_T{D}_T(V)+R(T,V)T=0$

The above is a second-order differential equations called the Jacobi equation.