TY - GEN
T1 - Hamiltonian non-displaceability of the Gauss images of isoprametric hypersurfaces (A survey)
AU - Miyaoka, Reiko
N1 - Funding Information:
Acknowledgements The author sincerely would like to thank Professor Young Jin Suh (Director of RIRCM) for his organization of twenty times successful workshops. The author also would like to thank Dr. Hyunjin Lee for her excellent supports to those workshops. The author is partly supported by JSPS Grant-in-Aid for Scientific Research (B) 615H036160.
Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2017.
PY - 2017
Y1 - 2017
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 -