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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quaternion Kaehlerian manifolds isometrically immersed in Euclidean space
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by M. Barros and F. Urbano PDF
Proc. Amer. Math. Soc. 89 (1983), 657-660 Request permission

Abstract:

Let $M$ be a complete $4n$-dimensional quaternion Kaehlerian manifold isometrically immersed in the $(4n + d)$-dimensional Euclidean space. In this note we prove that if $d < n$, then $M$ is a Riemannian product ${Q^m} \times P$, where ${Q^m}$ is the $m$-dimensional quaternion Euclidean space $(m \geqslant n - d)$ and $P$ is a Ricci flat quaternion Kaehlerian manifold.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 657-660
  • MSC: Primary 53C42; Secondary 53C55
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0718992-X
  • MathSciNet review: 718992