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Transactions of the American Mathematical Society

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Euler characters and submanifolds of constant positive curvature


Author: John Douglas Moore
Journal: Trans. Amer. Math. Soc. 354 (2002), 3815-3834
MSC (2000): Primary 53C40; Secondary 57R20
DOI: https://doi.org/10.1090/S0002-9947-02-03043-X
Published electronically: May 7, 2002
MathSciNet review: 1911523
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Abstract: This article develops methods for studying the topology of submanifolds of constant positive curvature in Euclidean space. It proves that if $M^n$ is an $n$-dimensional compact connected Riemannian submanifold of constant positive curvature in ${\mathbb E}^{2n-1}$, then $M^n$ must be simply connected. It also gives a conformal version of this theorem.


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Additional Information

John Douglas Moore
Affiliation: Department of Mathematics, University of California, Santa Barbara, CA 93106
Email: moore@math.ucsb.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03043-X
Received by editor(s): March 28, 2001
Published electronically: May 7, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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