Higher order differential geometry and some related questions Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/pc289m58f

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  • A theory of higher order connections is developed as a reduction of the structure group of the jet bundle of sections of a smooth vector bundle. This definition leads naturally to higher order curvatures and covariant derivatives. Curvature Conditions for a second order partial differential operator to have constant coefficients in the top order part are given. Also obtained are results on the reduction of real analytic C-R structures to the Cauchy- Riemann equations on a complex manifold via complexification and the study of the convexity of tubular neighborhoods in it.
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