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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A generalization of minimal cones
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by Norio Ejiri PDF
Trans. Amer. Math. Soc. 276 (1983), 347-360 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • 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