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, Takemura and Takeuchi
(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
