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

DOI:
https://doi.org/10.1090/S0002-9947-96-01694-7

MathSciNet review:
1370639

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Abstract | References | Similar Articles | Additional Information

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 nor admit a minimal isometric immersion into any sphere if the degree of the immersion is less than , or less than , 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:
https://doi.org/10.1090/S0002-9947-96-01694-7

Keywords:
Minimal isometric immersions,
inhomogeneous spherical space forms

Received by editor(s):
August 22, 1995

Article copyright:
© Copyright 1996
American Mathematical Society