Swan's theorem verifies the equivalence between finitely generated projective modules over function algebras and smooth vector bundles. We define A((r))-maps that correspond to usual non-linear differential operators of degree r under the equivalence of Swan's theorem and thus generalize Swan's theorem to include non-linear differential operators as morphisms. An A((r))-manifold structure is introduced on the space of sections of a fiber bundle through charts with A((r))-maps as transition homeomorphisms. A characterization for all the smooth maps between the spaces of sections of vector bundles, whose kth derivatives are linear differential operators of degree r in each variable, is given in terms of A((r))-maps.
机构:
Zhejiang Normal Univ, Dept Math Sci, Jinhua 321004, Zhejiang, Peoples R ChinaZhejiang Normal Univ, Dept Math Sci, Jinhua 321004, Zhejiang, Peoples R China
Liu, Ziyao
Chen, Jiecheng
论文数: 0引用数: 0
h-index: 0
机构:
Zhejiang Normal Univ, Dept Math Sci, Jinhua 321004, Zhejiang, Peoples R ChinaZhejiang Normal Univ, Dept Math Sci, Jinhua 321004, Zhejiang, Peoples R China
Chen, Jiecheng
Fan, Dashan
论文数: 0引用数: 0
h-index: 0
机构:
Univ Wisconsin Milwaukee, Dept Math Sci, Milwaukee, WI 53201 USAZhejiang Normal Univ, Dept Math Sci, Jinhua 321004, Zhejiang, Peoples R China