Jet bundles with Cartan distributions are characterized as polarised N^r_π-contact manifolds of jet type via a recognition theorem in k-contact geometry.
Equivalence, Invariants and Symmetry
3 Pith papers cite this work, alongside 575 external citations. Polarity classification is still indexing.
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First-order ODEs with curvature K(x,u)=κ(x) are integrable by quadratures exactly when the associated linear operator L=d²/dx²+κ(x) has a non-zero Liouvillian solution, with Kovacic's algorithm deciding the rational-κ case.
Noether symmetries of time-dependent damped nonlinear multidimensional wave equations produce conservation of linear and angular momentum, with the algebra enlarging to a conformal subalgebra for particular damping and nonlinearity forms.
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Jet Bundles as Higher-Order Polarised $k$-Contact Manifolds
Jet bundles with Cartan distributions are characterized as polarised N^r_π-contact manifolds of jet type via a recognition theorem in k-contact geometry.