  In this manuscript we consider Intrinsic Stochastic Differential Equations on
manifolds and constrain it to a level set of a smooth function. Such type of
constraints are known as explicit algebraic constraints. The system of
differential equation and the algebraic constraints is, in combination, called
the Stochastic Differential Algebraic Equations (SDAEs). We consider these
equations on manifolds and present methods for computing the solution of SDAEs
on manifolds.
