International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 40, Pages 2553-2565
doi:10.1155/S016117120320329X
On fuzzy subbundles of vector bundles
Department of Mathematics (Pure and Applied), Rhodes University, Grahamstown 6140, South Africa
Received 27 March 2002
Copyright © 2003 V. Murali and G. Lubczonok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper considers fuzzy subbundles of a vector bundle. We
define the operations sum, product, tensor product, Hom, and intersection of fuzzy subbundles and in each case, we characterize the corresponding flag of vector subbundles. We then propose two alternative definitions of integrability on fuzzy subbundles of a given type and discuss their naturality, merits, and shortcomings. We do these here with a view to introduce and study integrable fuzzy subbundles of tangent bundles on manifolds and foliations in further papers.