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- W145463898 abstract "A class of minimal almost complex submanifolds of a Riemannian manifold $tilde{M}^{4n}$ with a parallel quaternionic structure Q, in particular of a 4-dimensional oriented Riemannian manifold, is studied. A notion of Kähler submanifold is defined. Any Kähler submanifold is pluriminimal. In the case of a quaternionic Kähler manifold $tilde{M}^{4n}$ of non zero scalar curvature, in particular, when $tilde{M}^4$ is an Einstein, non Ricci-flat, anti-self-dual 4-manifold, we give a twistor construction of Kähler submanifolds M 2n of maximal possible dimension 2n. More precisely, we prove that any such Kähler submanifold M 2n of $tilde{M}^{4n}$ is the projection of a holomorphic Legendrian submanifold $L^{2n} subsetmathcal{Z}$ of the twistor space $(mathcal{Z},mathcal{H})$ of $tilde{M}^{4n}$ , considered as a complex contact manifold with the natural holomorphic contact structure $mathcal{H} subset{T}mathcal{Z}$ . Any Legendrian submanifold of the twistor space $mathcal{Z}$ is defined by a generating holomorphic function. This is a natural generalization of Bryant’s construction of superminimal surfaces in S 4=ℍP 1." @default.
- W145463898 created "2016-06-24" @default.
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- W145463898 date "2004-01-28" @default.
- W145463898 modified "2023-10-06" @default.
- W145463898 title "A twistor construction of Kähler submanifolds of a quaternionic Kähler manifold" @default.
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- W145463898 doi "https://doi.org/10.1007/s10231-003-0089-x" @default.
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