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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Minimal submanifolds of $ E\sp {2n+1}$ arising from degenerate $ {\rm SO} (3)$ orbits on the Grassmannian


Author: J. M. Landsberg
Journal: Trans. Amer. Math. Soc. 325 (1991), 101-117
MSC: Primary 53C42; Secondary 58E20
MathSciNet review: 1012515
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Abstract: We give new examples of minimal submanifolds of $ {{\mathbf{E}}^{2n + 1}}$ characterised by having their Gauss map's image lie in degenerate $ SO(3)$ orbits of $ {G_{p,2n + 1}}$, the Grassmannian of $ p$-planes in $ {{\mathbf{E}}^{2n + 1}}$ (where the action on $ {G_{p,2n + 1}}$ is induced from the irreducible $ SO(3)$ action on $ {{\mathbf{R}}^{2n + 1}}$). These submanifolds are all given explicitly in terms of holomorphic data and are linearly full in $ {{\mathbf{E}}^{2n + 1}}$.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1012515-5
Keywords: Minimal submanifolds, calibrations
Article copyright: © Copyright 1991 American Mathematical Society