Hokkaido Mathematical Journal

KAJISA Tomonori,

On the existence of local frames of CR vector bundles.

Hokkaido Mathematical Journal, 42 (2013) pp.121-130

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Abstract

Given a CR manifold D, we shall show that existence of a CR local frame of a certain CR vector bundle over D is equivalent to the local imbeddability of D. This will imply that there exists a CR vector bundle which doesn't have CR local frames. Using this bundle, we shall construct CR line bundles over 3-dimensional non-imbeddable CR manifolds which don't have CR local frames.

MSC(Primary)32V99
MSC(Secondary)
Uncontrolled KeywordsCR manifold, CR imbedding, CR vector bundle