Abstract
In this paper we study the deformation theory of submanifolds characterized by a system of differential forms and provide a criterion for deformations of such submanifolds to be unobstructed. We apply this deformation theory to special Legendrian submanifolds in Sasaki–Einstein manifolds. In general, special Legendrian deformations have the obstruction. However, we show that the deformation space of special Legendrian submanifolds is the intersection of two larger smooth deformation spaces of different types. We also prove that any special Legendrian submanifold admits smooth deformations, which are not special Legendrian deformations, given by harmonic 1-forms.
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Acknowledgments
The author would like to thank the referee for his useful comments. This work was partially supported by GCOE ‘Fostering top leaders in mathematics’, Kyoto University and by Grant-in-Aid for Young Scientists (B) \(\sharp \)21740051 from JSPS.
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Moriyama, T. Deformations of special Legendrian submanifolds in Sasaki–Einstein manifolds. Math. Z. 283, 1111–1147 (2016). https://doi.org/10.1007/s00209-016-1635-8
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DOI: https://doi.org/10.1007/s00209-016-1635-8