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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
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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Keywords: Minimal cone, cohomogeneity, catenoid, warped product, Sasakian structure, <IMG WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\Phi$">-holomorphic sectional curvature, totally real submanifold
Article copyright: © Copyright 1983 American Mathematical Society