We give a new description of N=1 super Yang-Mills theory in curved
superspace. It is based on the induced geometry approach to a curved superspace
in which it is viewed as a surface embedded into C(4|2). The complex structure
on C(4|2) supplied with a standard volume element induces a special
Cauchy-Riemann (SCR)-structure on the embedded surface. We give an explicit
construction of SYM theory in terms of intrinsic geometry of the superspace
defined by this SCR-structure and a CR-bundle over the superspace. We write a
manifestly SCR-covariant Lagrangian for SYM coupled with matter. We also show
that in a special gauge our formulation coincides with the standard one which
uses Lorentz connections. Some useful auxiliary results about the integration
over surfaces in superspace are obtained.Comment: 16 pages, Late
