In this paper, we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits. As an application, we give a Kastler-Kalau-Walze type theorem for foliations.
D. ArcaraDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112Yuan-Pin LeeDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112