Tsukuba Journal of Mathematics

Examples of transversally complex submanifolds of the associative Grassmann manifold

Kanako Enoyoshi and Kazumi Tsukada

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Abstract

We consider the Grassmann manifold of associative subspaces in the space of imaginary octonions, which we call the associative Grassmann manifold. It is known that the associative Grassmann manifold is an eight-dimensional compact symmetric quaternionic Kähler manifold. We construct interesting examples of four-dimensional complex submanifolds of the associative Grassmann manifold.

Article information

Source
Tsukuba J. Math., Volume 43, Number 1 (2019), 23-36.

Dates
First available in Project Euclid: 25 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1571968819

Digital Object Identifier
doi:10.21099/tkbjm/1571968819

Mathematical Reviews number (MathSciNet)
MR4023312

Subjects
Primary: 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry
Secondary: 53B25: Local submanifolds [See also 53C40]

Keywords
the associative Grassmann manifold a quaternionic Kähler manifold transversally complex submanifolds totally complex submanifolds

Citation

Enoyoshi, Kanako; Tsukada, Kazumi. Examples of transversally complex submanifolds of the associative Grassmann manifold. Tsukuba J. Math. 43 (2019), no. 1, 23--36. doi:10.21099/tkbjm/1571968819. https://projecteuclid.org/euclid.tkbjm/1571968819


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