TY - GEN

T1 - Hamiltonian non-displaceability of the Gauss images of isoprametric hypersurfaces (A survey)

AU - Miyaoka, Reiko

PY - 2017/1/1

Y1 - 2017/1/1

N2 - This is a survey of the joint work [13] (Bull Lond Math Soc 48(5), 802–812, 2016) with Hiroshi Iriyeh (Ibaraki U.), Hui Ma (Tsinghua U.) and Yoshihiro Ohnita (Osaka City U.). The Floer homology of Lagrangian intersections is computed in few cases. Here, we take the image L=G(N) of the Gauss map of isoparametric hypersurfaces N in Sn+1, that are minimal Lagrangian submanifolds of the complex hyperquadric Qn(ℂ). We call L Hamiltonian non-displaceable if L∩ φ (L)≠ ∅ holds for any Hamiltonian deformation φ. Hamiltonian non-displaceability is needed to define the Floer homology HF(L), since HF(L) is generated by points in L∩ φ (L). We prove the Hamiltonian non-displaceability of L=G(N) for any isoparametric hypersurfaces N with principal curvatures having plural multiplicities. The main result is stated in Sect. 4.

AB - This is a survey of the joint work [13] (Bull Lond Math Soc 48(5), 802–812, 2016) with Hiroshi Iriyeh (Ibaraki U.), Hui Ma (Tsinghua U.) and Yoshihiro Ohnita (Osaka City U.). The Floer homology of Lagrangian intersections is computed in few cases. Here, we take the image L=G(N) of the Gauss map of isoparametric hypersurfaces N in Sn+1, that are minimal Lagrangian submanifolds of the complex hyperquadric Qn(ℂ). We call L Hamiltonian non-displaceable if L∩ φ (L)≠ ∅ holds for any Hamiltonian deformation φ. Hamiltonian non-displaceability is needed to define the Floer homology HF(L), since HF(L) is generated by points in L∩ φ (L). We prove the Hamiltonian non-displaceability of L=G(N) for any isoparametric hypersurfaces N with principal curvatures having plural multiplicities. The main result is stated in Sect. 4.

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U2 - 10.1007/978-981-10-5556-0_8

DO - 10.1007/978-981-10-5556-0_8

M3 - Conference contribution

AN - SCOPUS:85030180210

SN - 9789811055553

T3 - Springer Proceedings in Mathematics and Statistics

SP - 83

EP - 99

BT - Hermitian-Grassmannian Submanifolds

A2 - Ohnita, Yoshihiro

A2 - Zhou, Jiazu

A2 - Hak Kim, Byung

A2 - Lee, Hyunjin

A2 - Jin Suh, Young

PB - Springer New York LLC

T2 - 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, IWHSSS 2016

Y2 - 26 July 2016 through 30 July 2016

ER -