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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120320329X |
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| _version_ | 1832554510075035648 |
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| author | V. Murali G. Lubczonok |
| author_facet | V. Murali G. Lubczonok |
| author_sort | V. Murali |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-97ec2e7b470a403fb669213936729884 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-97ec2e7b470a403fb6692139367298842025-02-03T05:51:18ZengWileyInternational 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 |
| spellingShingle | V. Murali G. Lubczonok On fuzzy subbundles of vector bundles International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | On fuzzy subbundles of vector bundles |
| title_sort | on fuzzy subbundles of vector bundles |
| url | http://dx.doi.org/10.1155/S016117120320329X |
| work_keys_str_mv | AT vmurali onfuzzysubbundlesofvectorbundles AT glubczonok onfuzzysubbundlesofvectorbundles |