Contact Calabi-Yau manifolds and Special Legendrian submanifolds

Abstract

We consider a generalization of Calabi-Yau structures in the context of $\alpha$-Sasakian manifolds. We study deformations of a special class of Legendrian submanifolds and classify invariant contact Calabi-Yau structures on 5-dimensional nilmanifolds. Finally we generalize to codimension $r$.

16 pages, no figures. Final version to appear in "Osaka J. Math."

References in corpus (2)

• On Eta-Einstein Sasakian Geometry
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds