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Transactions of the American Mathematical Society

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

 

 

Minimal hypersurfaces of $ {\bf R}\sp {2m}$ invariant by $ {\rm SO}(m)\times {\rm SO}(m)$


Author: Hilário Alencar
Journal: Trans. Amer. Math. Soc. 337 (1993), 129-141
MSC: Primary 53C42
DOI: https://doi.org/10.1090/S0002-9947-1993-1091229-1
MathSciNet review: 1091229
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Abstract: Let $ G = {\text{SO}}(m) \times {\text{SO}}(m)$ act in the standard way on $ {{\mathbf{R}}^m} \times {{\mathbf{R}}^m}$. We describe all complete minimal hypersurfaces of $ {{\mathbf{R}}^m}\backslash \{ 0\} $ which are invariant under $ G$ for $ m = 2$, $ 3$ . We also show that the unique minimal hypersurface of $ {{\mathbf{R}}^{2m}}$ which is invariant under $ G$ and passes through the origin of $ {{\mathbf{R}}^{2m}}$ is the minimal quadratic cone.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1091229-1
Keywords: Minimal hypersurface, orbit space, invariant hypersurface, minimal quadratic cone
Article copyright: © Copyright 1993 American Mathematical Society