Tangent bundle geometry induced by second order partial differential equations

D. J. Saunders; O. Rossi; G. E. Prince

doi:10.1016/j.matpur.2016.02.011

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arXiv · 1412.2377

Tangent bundle geometry induced by second order partial differential equations

D. J. Saunders·O. Rossi·G. E. Prince

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Abstract

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent variables, together with a transverse local vector field. The resulting decomposition provides several natural curvature operators. The harmonic map equation is examined, and in this case both the 1-form and the vector field arise naturally.

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BibTeX RIS

D. J. Saunders, O. Rossi, G. E. Prince. 2014-12-07. Tangent bundle geometry induced by second order partial differential equations. https://doi.org/10.1016/j.matpur.2016.02.011

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