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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0718992-X
PII: S 0002-9939(1983)0718992-X
Article copyright: © Copyright 1983 American Mathematical Society