Advanced Studies in Pure Mathematics

Moment map of the spin action and the Cartan-Münzner Polynomials

Reiko Miyaoka

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Abstract

We describe the Cartan-Münzner polynomials of degree four on an $N$-dimensional Euclidean space by using the square norm of the moment map of certain group actions. In the case of OT-FKM type, the action is a spin action which is not necessarily transitive on isoprametric hypersurfaces.

Article information

Source
Differential Geometry and Tanaka Theory — Differential System and Hypersurface Theory —, T. Shoda and K. Shibuya, eds. (Tokyo: Mathematical Society of Japan, 2019), 1-11

Dates
Received: 12 May 2012
Revised: 4 April 2013
First available in Project Euclid: 27 November 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1574872397

Digital Object Identifier
doi:10.2969/aspm/08210001

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C24: Rigidity results 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Keywords
isoparametric hypersurfaces moment map

Citation

Miyaoka, Reiko. Moment map of the spin action and the Cartan-Münzner Polynomials. Differential Geometry and Tanaka Theory — Differential System and Hypersurface Theory —, 1--11, Mathematical Society of Japan, Tokyo, Japan, 2019. doi:10.2969/aspm/08210001. https://projecteuclid.org/euclid.aspm/1574872397


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