The almost complex (para-complex) structures on 6-pseudo-Riemannian spheres and related Schrödinger flows

Zhong, Shiping

doi:10.1007/s40627-020-00042-z

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The Case Of the Imaginary Part Im(o) Of The Octonions1

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2021

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“…We have furthered our understanding of almost complex structures on S 6 and the G 2 -structure on Im(O) = R 7 via Schrödinger flows. One may give a similar discussion in the imaginary part of the split octonions (see [72]). However, many related problems remain to be clarified.…”

Section: The Case Of the Imaginary Part Im(o) Of The Octonionsmentioning

confidence: 89%

On the vortex filament in 3-spaces and its generalizations

Ding

Zhong

2021

Sci. China Math.

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In this article, we devote to a mathematical survey on the theory of the vortex filament in 3dimensional spaces and its generalizations. We shall present some effective geometric tools applied in the study, such as the Schrödinger flow, the geometric Korteweg-de Vries (KdV) flow and the generalized bi-Schrödinger flow, as well as the complex and para-complex structures. It should be mentioned that the investigation in the imaginary part of the octonions looks very fascinating, since it relates to almost complex structures and the G 2 structure on S 6 . As a new result in this survey, we describe the equation of generalized bi-Schrödinger flows from R 1 into a Riemannian surface.

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Section: The Case Of the Imaginary Part Im(o) Of The Octonionsmentioning

confidence: 89%