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

Commun. Korean Math. Soc. 2002 Vol. 17, No. 4, 635-645 Printed December 1, 2002

J.S. Kim, J.H. Cho, M. M. Tripathi, R. Prasad Sunchon National University, Sunchon National University, Lucknow University, Lucknow University

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.