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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Minimal isometric immersions of inhomogeneous spherical space forms into spheres---
a necessary condition for existence


Author: Christine M. Escher
Journal: Trans. Amer. Math. Soc. 348 (1996), 3713-3732
MSC (1991): Primary 53C42
MathSciNet review: 1370639
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Abstract: Although much is known about minimal isometric immersions into spheres of homogeneous spherical space forms, there are no results in the literature about such immersions in the dominant case of inhomogeneous space forms. For a large class of these, we give a necessary condition for the existence of such an immersion of a given degree. This condition depends only upon the degree and the fundamental group of the space form and is given in terms of an explicitly computable function. Evaluating this function shows that neither $L(5,2)$ nor $L(8,3)$ admit a minimal isometric immersion into any sphere if the degree of the immersion is less than $28$, or less than $20$, respectively.


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Additional Information

Christine M. Escher
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email: tine@math.orst.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01694-7
PII: S 0002-9947(96)01694-7
Keywords: Minimal isometric immersions, inhomogeneous spherical space forms
Received by editor(s): August 22, 1995
Article copyright: © Copyright 1996 American Mathematical Society