Let be $M$ a Riemannian manifold and $X,Y$ vector fields over $M.$ Now take $p\in M$ arbitrarily, my question is, how construc a variation $f:U\to M,$ $U\subset \mathbb{R}^2,~~U=\{-\epsilon
$\dfrac{\partial f}{\partial t}(0,1)=X(p),~~~\dfrac{\partial f}{\partial s}(0,1)= Y(p)~~~~~~ ??$