Translator Disclaimer
March 2020 Lagrangian submanifolds of $S^6$ and the associative Grassmann manifold
Kanako Enoyoshi, Kazumi Tsukada
Kodai Math. J. 43(1): 170-192 (March 2020). DOI: 10.2996/kmj/1584345693

Abstract

We focus on Lagrangian submanifolds of a six-dimensional sphere in the space Im $\mathbf {O}$ of imaginary octonions and study the relationship of such submanifolds with the geometry of the associative Grassmann manifold $\widetilde{{\rm Gr}}_{ass}$(Im $\mathbf {O}$) which is the Grassmann manifold of associative subspaces in Im $\mathbf {O}$. Considering the Gauss maps into $\widetilde{{\rm Gr}}_{ass}$(Im $\mathbf {O}$) associated to Lagrangian submanifolds, we show that those maps are harmonic. Moreover, the Gauss maps associated to homogeneous Lagrangian submanifolds are investigated.

Citation

Download Citation

Kanako Enoyoshi. Kazumi Tsukada. "Lagrangian submanifolds of $S^6$ and the associative Grassmann manifold." Kodai Math. J. 43 (1) 170 - 192, March 2020. https://doi.org/10.2996/kmj/1584345693

Information

Published: March 2020
First available in Project Euclid: 16 March 2020

zbMATH: 07196515
MathSciNet: MR4077210
Digital Object Identifier: 10.2996/kmj/1584345693

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

JOURNAL ARTICLE
23 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.43 • No. 1 • March 2020
Back to Top