Minimal Maslov number of $R$-spaces canonically embedded in Einstein-Kähler $C$-spaces | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Minimal Maslov number of $R$-spaces canonically embedded in Einstein-Kähler $C$-spaces

De Yoshihiro Ohnita

Apparaît dans la collection : Problèmes variationnels et géométrie des sous-variétés / Variational Problems and the Geometry of Submanifolds

An $R$-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each $R$-space has the canonical embedding into a Kähler $C$-space as a real form which is a compact embedded totally geodesic Lagrangian submanifold. The minimal Maslov number of Lagrangian submanifolds in symplectic manifolds is an invariant under Hamiltonian isotopies and very fundamental to the study of the Floer homology for intersections of Lagrangian submanifolds. In this talk we provide a Lie theoretic formula for the minimal Maslov number of $R$-spaces canonically embedded in Einstein-Kähler $C$-spaces and discuss several examples of the calculation by the formula.

Informations sur la vidéo

Date de captation 29/05/2019
Date de publication 18/06/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19533103
Citer cette vidéo Ohnita, Yoshihiro (29/05/2019). Minimal Maslov number of $R$-spaces canonically embedded in Einstein-Kähler $C$-spaces. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19533103
URL https://dx.doi.org/10.24350/CIRM.V.19533103

Domaine(s)

Bibliographie

BOREL, Armand et HIRZEBRUCH, Friedrich. Characteristic classes and homogeneous spaces, I. American Journal of Mathematics, 1958, vol. 80, no 2, p. 458-538. - https://doi.org/10.2307/2372795
ONO, Hajime. Integral formula of Maslov index and its applications. Japanese journal of mathematics. New series, 2004, vol. 30, no 2, p. 413-421. - https://doi.org/10.4099/math1924.30.413
SATAKE, Ichirô. On representations and compactifications of symmetric Riemannian spaces. Annals of Mathematics, 1960, p. 77-110. - https://doi.org/10.2307/1969880
TAKEUCHI, Masaru. Cell decompositions and Morse equalities on certain symmetric spaces. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 1965, vol. 12, p. 81-192.
TAKEUCHI, Masaru, KOBAYASHI, Shoshichi, et al. Minimal imbeddings of $ R $-spaces. Journal of Differential Geometry, 1968, vol. 2, no 2, p. 203-215. - https://doi.org/10.4310/jdg/1214428257
TAKEUCHI, Masaru. Homogeneous Kähler submanifolds in complex projective spaces. Japanese journal of mathematics. New series, 1978, vol. 4, no 1, p. 171-219. - https://doi.org/10.4099/math1924.4.171
TAKEUCHI, Masaru. Stability of certain minimal submanifolds of compact Hermitian symmetric spaces. Tohoku Mathematical Journal, Second Series, 1984, vol. 36, no 2, p. 293-314. - https://doi.org/10.2748/tmj/1178228853
OHNITA, Yoshihiro. Minimal Maslov number of $R$-spaces canonically embedded in Einstein-Kähler $C$-spaces. Preprint submitted to Complex Manifolds. OCAMI Preprint Ser. 18-8. - http://www.sci.osaka-cu.ac.jp/OCAMI/publication/preprint/pdf2018/18_08.pdf
OHNITA, YOSHIHIRO. Geometry of Lagrangian submanifolds and isoparametric hypersurfaces. In : Proceedings of The Fourteenth International Workshop on Differential Geometry. 2010. p. 43-67. - http://www.sci.osaka-cu.ac.jp/~ohnita/paper/2010OhnitaProcKNUGRG.pdf
MA, Hui, OHNITA, Yoshihiro, et al. Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces, I. Journal of Differential Geometry, 2014, vol. 97, no 2, p. 275-348. - https://doi.org/10.4310/jdg/1405447807
IRIYEH, Hiroshi, MA, Hui, MIYAOKA, Reiko, et al. Hamiltonian non‐displaceability of Gauss images of isoparametric hypersurfaces. Bulletin of the London Mathematical Society, 2016, vol. 48, no 5, p. 802-812. - https://doi.org/10.1112/blms/bdw040

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/1936/Slides/ohnita.pdf

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2024

Donner son avis