This article presents a differential geometrical method for analyzing sequential test procedures. It is based on the primal result on the conformal geometry of statistical manifold developed in Kumon et al. (0012"> 2011). By introducing curvature-type random variables, the condition is first clarified for a statistical manifold to be an exponential family under an appropriate sequential test procedure. This result is further elaborated for investigating the efficient sequential test in a multidimensional curved exponential family. The theoretical results are numerically examined by using von Mises-Fisher and hyperboloid models.