  We introduce the notion of affine Legendrian submanifolds in Sasakian
manifolds and define a canonical volume called the $\phi$-volume as odd
dimensional analogues of affine Lagrangian (totally real or purely real)
geometry. Then we derive the second variation formula of the $\phi$-volume to
obtain the stability result in some $\eta$-Einstein Sasakian manifolds. It also
implies the convexity of the $\phi$-volume functional on the space of affine
Legendrian submanifolds. Next, we introduce the notion of special affine
Legendrian submanifolds in Sasaki-Einstein manifolds as a generalization of
that of special Legendrian submanifolds. Then we show that the moduli space of
compact connected special affine Legendrian submanifolds is a smooth
Fr\'{e}chet manifold.
