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On automorphism groups of an $\epsilon $-framed manifold

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Abstract

Two examples of $\epsilon $-framed manifolds are constructed. It is proved that an $\epsilon $-framed structure on a manifold is not unique. Automorphism groups of $\epsilon $-framed manifolds are studied. Lastly we prove that a connected Lie group $G$ admits a left invariant normal $ \epsilon $-framed structure if and only if the Lie algebra of all left invariant vector fields on $G$ is an $\epsilon $-framed Lie algebra.

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