On the existence of complete parallel vector fields

Welsh, David J.

doi:10.1090/S0002-9939-1986-0835888-6

On the existence of complete parallel vector fields
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by David J. Welsh PDF

Proc. Amer. Math. Soc. 97 (1986), 311-314 Request permission

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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