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On compositions of conformal immersions


Authors: Marcos Dajczer and Enaldo Vergasta
Journal: Proc. Amer. Math. Soc. 118 (1993), 211-215
MSC: Primary 53C42; Secondary 53A30
DOI: https://doi.org/10.1090/S0002-9939-1993-1164141-2
MathSciNet review: 1164141
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Abstract: We consider conformal immersions of a manifold $ {M^n},\;n \geqslant 6$, into conformally flat manifolds. If the principal curvatures of $ f:{M^n} \to N_{cf}^{n + 1}$ have multiplicities at most $ n - 4$, we show that any $ g:{M^n} \to \tilde N_{cf}^{n + 2}$ can locally be written as $ g = \rho \circ f$, where $ \rho :N_{cf}^{n + 1} \to \tilde N_{cf}^{n + 2}$ is a conformal immersion.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1164141-2
Article copyright: © Copyright 1993 American Mathematical Society

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