Osaka Journal of Mathematics

Deformations of special Legendrian submanifolds with boundary

Guangcun Lu and Xiaomin Chen

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Abstract

In this paper, for a compact special Legendrian submanifold with smooth 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 call a scafford (Definition 2.3) by analogy with Butsher [1]. 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 closed case considered by Tomassini and Vezzoni [17].

Article information

Source
Osaka J. Math., Volume 51, Number 3 (2014), 673-695.

Dates
First available in Project Euclid: 23 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1414090798

Mathematical Reviews number (MathSciNet)
MR3272612

Zentralblatt MATH identifier
1314.53083

Subjects
Primary: 53C10: $G$-structures 53D10: Contact manifolds, general 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C38: Calibrations and calibrated geometries

Citation

Lu, Guangcun; Chen, Xiaomin. Deformations of special Legendrian submanifolds with boundary. Osaka J. Math. 51 (2014), no. 3, 673--695. https://projecteuclid.org/euclid.ojm/1414090798


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