Special Legendrian submanifolds in toric Sasaki-Einstein manifolds
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Publication:2353166
zbMath1322.53054arXiv1201.1080MaRDI QIDQ2353166
Publication date: 8 July 2015
Published in: The New York Journal of Mathematics (Search for Journal in Brave)
Abstract: We show that every toric Sasaki-Einstein manifold $S$ admits a special Legendrian submanifold $L$ which arises as the link ${
m fix}( au)cap S$ of the fixed point set ${
m fix}( au)$ of an anti-holomorphic involution $ au$ on the cone $C(S)$. In particular, an irregular toric Sasaki-Einstein manifold $S^{2} imes S^{3}$ has a special Legendrian torus $S^{1} imes S^{1}$. Moreover, we also obtain a special Legendrian submanifold in $sharp m(S^{2} imes S^{3})$ for each $mge 1$.
Full work available at URL: https://arxiv.org/abs/1201.1080
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Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global submanifolds (53C40) Calibrations and calibrated geometries (53C38)
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