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Transactions of the American Mathematical Society

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

 

 

On some real hypersurfaces of a complex projective space


Author: Masafumi Okumura
Journal: Trans. Amer. Math. Soc. 212 (1975), 355-364
MSC: Primary 53C55; Secondary 32C10
DOI: https://doi.org/10.1090/S0002-9947-1975-0377787-X
MathSciNet review: 0377787
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Abstract: A principal circle bundle over a real hypersurface of a complex projective space $ C{P^n}$ can be regarded as a hypersurface of an odd-dimensional sphere. From this standpoint we can establish a method to translate conditions imposed on a hypersurface of $ C{P^n}$ into those imposed on a hypersurface of $ {S^{2n + 1}}$. Some fundamental relations between the second fundamental tensor of a hypersurface of $ C{P^n}$ and that of a hypersurface of $ {S^{2n + 1}}$ are given.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0377787-X
Keywords: Submersion, fundamental tensor of submersion, second fundamental tensor, lift
Article copyright: © Copyright 1975 American Mathematical Society