Tsukuba Journal of Mathematics

Examples of transversally complex submanifolds of the associative Grassmann manifold

Kanako Enoyoshi and Kazumi Tsukada

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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

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

First available in Project Euclid: 25 October 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

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


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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