On fuzzy subbundles of vector bundles

On fuzzy subbundles of vector bundles

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 fu...

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Main Authors: V. Murali, G. Lubczonok
Format: Article
Language:English
Published: Hindawi Limited 2003-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S016117120320329X
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spelling doaj-97ec2e7b470a403fb6692139367298842020-11-25T00:25:30ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003402553256510.1155/S016117120320329XOn fuzzy subbundles of vector bundlesV. Murali0G. Lubczonok1Department of Mathematics (Pure and Applied), Rhodes University, Grahamstown 6140, South AfricaDepartment of Mathematics (Pure and Applied), Rhodes University, Grahamstown 6140, South AfricaThis 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.http://dx.doi.org/10.1155/S016117120320329X
collection DOAJ
language English
format Article
sources DOAJ
author V. Murali
G. Lubczonok
spellingShingle V. Murali
G. Lubczonok
On fuzzy subbundles of vector bundles
International Journal of Mathematics and Mathematical Sciences
author_facet V. Murali
G. Lubczonok
author_sort V. Murali
title On fuzzy subbundles of vector bundles
title_short On fuzzy subbundles of vector bundles
title_full On fuzzy subbundles of vector bundles
title_fullStr On fuzzy subbundles of vector bundles
title_full_unstemmed On fuzzy subbundles of vector bundles
title_sort on fuzzy subbundles of vector bundles
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2003-01-01
description 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.
url http://dx.doi.org/10.1155/S016117120320329X
work_keys_str_mv AT vmurali onfuzzysubbundlesofvectorbundles
AT glubczonok onfuzzysubbundlesofvectorbundles
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