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Quaternion Kaehlerian manifolds isometrically immersed in Euclidean space


Authors: M. Barros and F. Urbano
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
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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.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1983-0718992-X
Article copyright: © Copyright 1983 American Mathematical Society

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