In this article, for a compact special Legendrian submanifold withboundary of contact Calabi-Yau manifolds we study the deformationof it with boundary confined in an appropriately chosen contactsubmanifold of codimension two which we also call a scafford(Definition 4) by analogy with Butsher.Our result shows that it cannot bedeformed under such a boundary confinement. This result may be viewedas supplements of the compact boundless case considered by Tomassini andVezzoni.
Research Fund for theDoctoral Program Higher Education of China （200800270003）
The first author is supported by NationalNatural Science Foundation （Grant No. 10971014）
School of Mathematical Sciences, Beijing Normal University, Beijing 100875,Department of Mathematics, China University of Petroleum, Beijing 102249