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 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

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Geometric fuzzification

Abstract unavailable at this time... Mathematics Subject Classification (2000): 03E72, 52A01, 54E35, 53C70, 14M15 Quaestiones Mathematicae 25 (2002), 147-16

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© Hindawi Publishing Corp. 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 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