Deformations of Special Legendrian Submanifolds with Boundary

Details Deformations of Special Legendrian Submanifolds with Boundary Deformations of Special Legendrian Submanifolds with Boundary

2011-06-25

arxiv.org/abs/1106.5086v1

Mathematics

Differential Geometry

Latex, 19 pages

Scientific paper

In this article, for a compact special Legendrian submanifold with boundary of contact Calabi-Yau manifolds we study the deformation of it with boundary confined in an appropriately chosen contact submanifold of codimension two which we also a scafford (Definition \ref{def:2.3}) by analogy with [A.Butsher, Deformations of minimal Lagrangian submanifolds with boundary, Proc. Amer. Math. Soc. 131(2002) 1953-1964]. Our first result shows that it cannot be deformed, and the second claims that deformations of such a special Legendrian submanifold forms a one-dimensional smooth manifold under suitably weaker boundary confinement conditions. They may be viewed as supplements of the boundless case considered by Tomassini and Vezzoni [Contact Calabi-Yau manifolds and special Legendrian submanifolds, Osaka J. Math., 45(2008), 127-147].

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