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Transactions of the American Mathematical Society

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

 

 

A generalization of minimal cones


Author: Norio Ejiri
Journal: Trans. Amer. Math. Soc. 276 (1983), 347-360
MSC: Primary 53C42
DOI: https://doi.org/10.1090/S0002-9947-1983-0684514-X
MathSciNet review: 684514
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Abstract: Let $ {R_ +}$ be a positive real line, $ {S^n}$ an $ n$-dimensional unit sphere. We denote by $ {R_+} \times {S^n}$ the polar coordinate of an $ (n + 1)$-dimensional Euclidean space $ {R^{n + 1}}$. It is well known that if $ M$ is a minimal submanifold in $ {S^n}$, then $ {R_ +} \times M$ is minimal in $ {R^{n + 1}}$. $ {R_+} \times M$ is called a minimal cone. We generalize this fact and give many minimal submanifolds in real and complex space forms.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0684514-X
Keywords: Minimal cone, cohomogeneity, catenoid, warped product, Sasakian structure, $ \Phi $-holomorphic sectional curvature, totally real submanifold
Article copyright: © Copyright 1983 American Mathematical Society