Français
Minimal Maslov number of $R$-spaces canonically embedded in Einstein-Kähler $C$-spaces
Multi angle
Authors : Ohnita, Yoshihiro (Author of the conference)
CIRM (Publisher )
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C55 - Hermitian and Kählerian manifolds (global differential geometry)
Additional resources :
https://www.cirm-math.fr/RepOrga/1936/Slides/ohnita.pdf
CIRM (Publisher )
Loading the player...
|
Abstract :
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.
Keywords : $R$-spaces; Eintein-Kähler $C$-spaces; monotone Lagrangian submanifolds; minimal Maslov number
MSC Codes : Keywords : $R$-spaces; Eintein-Kähler $C$-spaces; monotone Lagrangian submanifolds; minimal Maslov number
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C55 - Hermitian and Kählerian manifolds (global differential geometry)
Additional resources :
https://www.cirm-math.fr/RepOrga/1936/Slides/ohnita.pdf
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/06/2019 Conference Date : 29/05/2019 Subseries : Research talks arXiv category : Differential Geometry ; Symplectic Geometry Mathematical Area(s) : Geometry Format : MP4 (.mp4) - HD Video Time : 00:59:10 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-05-29_Ohnita.mp4 
|
Information on the Event
Event Title : Problèmes variationnels et géométrie des sous-variétés / Variational Problems and the Geometry of SubmanifoldsEvent Organizers : Alias, Luis J. ; Loubeau, Eric ; Mazet, Laurent ; Montaldo, Stefano ; Soret, Marc ; Ville, Marina Dates : 27/05/2019 - 31/05/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/1936.html
Citation Data
DOI : 10.24350/CIRM.V.19533103Cite this video as: Ohnita, Yoshihiro (2019). Minimal Maslov number of $R$-spaces canonically embedded in Einstein-Kähler $C$-spaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19533103 URI : http://dx.doi.org/10.24350/CIRM.V.19533103 |
See Also
- [Multi angle] Singularities of Teichmüller harmonic map flow / Author of the conference Rupflin, Melanie.
- [Post-edited] $L^2$ curvature for surfaces in Riemannian manifolds / Author of the conference Kuwert, Ernst.
- [Multi angle] Willmore stability and conformal rigidity of minimal surfaces in $\mathbb{S}^{n}$ / Author of the conference Kusner, Rob.
Bibliography
- 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
