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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the existence of complete parallel vector fields


Author: David J. Welsh
Journal: Proc. Amer. Math. Soc. 97 (1986), 311-314
MSC: Primary 53C20; Secondary 53C05, 57R25
DOI: https://doi.org/10.1090/S0002-9939-1986-0835888-6
MathSciNet review: 835888
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Abstract: In 1966, Chern asked which compact orientable manifolds carry a Riemannian metric and a vector field which is parallel under this metric. An earlier paper answered this without assuming orientability. The present paper applies techniques which work without compactness to identify manifolds which can carry complete parallel vector fields


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DOI: https://doi.org/10.1090/S0002-9939-1986-0835888-6
Article copyright: © Copyright 1986 American Mathematical Society