It is  well known that   TS^n-1 is diffeomorphic to M= f^{-1}(1) where 
f:C^n---->C, f=\sum_{i=1}^{n} z_{i}^{2}.
two question:
1)Is  M  a  symplectic  submanifold of C^n ~ R^2n (with the standard symplectic structure)?

 if  the answer is affirmative, we can consider two  symplectic structure for TS^n-1. The first is the original structure of the tangent or  cotangent bundle, the second one is the  pull back  structure of  M

2)are these structures equivalent?