Nonlinear Distributional Geometry
نویسندگان
چکیده
Colombeau’s construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A pointvalue characterization for generalized functions on manifolds is derived, several algebraic characterizations of spaces of generalized sections are established and consistency properties with respect to linear distributional geometry are derived. An application to nonsmooth mechanics indicates the additional flexibility offered by this approach compared to the purely distributional picture. Mathematics Subject Classification (2000): Primary: 46F30; secondary: 46T30, 46F10, 37J05.
منابع مشابه
Nonlinear distributional geometry and general relativity
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau’s special setting) and its applications to general relativity with a special focus on the distributional description of impulsive gravitational waves.
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We discuss some basic concepts of semi-Riemannian geometry in low-regularity situations. In particular, we compare the settings of (linear) distributional geometry in the sense of L. Schwartz and nonlinear distributional geometry in the sense of J.F. Colombeau. AMS Mathematics Subject Classification (2000): Primary: 83C75; secondary: 46T30, 53B30, 46F10, 46F30.
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