Differential p-forms and q-vector fields with constant coefficients are studied. Differential p-forms of degrees p = 1, 2, n – 1, n with constant coefficients on a smooth n-dimensional manifold M are characterized. In the contravariant case, the obstruction for a q-vector field V-q to have constant coefficients is proved to be the Schouten-Nijenhuis bracket of V-q with itself. The q-vector fields with constant coefficients of degrees q = 1, 2, n – 1, n are also characterized. The notions of differential p-forms and q-vector fields with conformal constant coefficients are introduced. For arbitrary degrees p and q, such differential p-forms and q-vector fields are seen to be the solutions to two second-order partial differential systems on J(2)(M, R-n), which are reducible to two first-order partial differential systems by adding variables. Computational aspects in solving these systems are discussed and examples and applications are also given.
Differential p-forms and q-vector fields with constant coefficients are studied. Differential p-forms of degrees p = 1, 2, n – 1, n with constant coefficients on a smooth n-dimensional manifold M are characterized. In the contravariant case, the obstruction for a q-vector field V-q to have constant coefficients is proved to be the Schouten-Nijenhuis bracket of V-q with itself. The q-vector fields with constant coefficients of degrees q = 1, 2, n – 1, n are also characterized. The notions of differential p-forms and q-vector fields with conformal constant coefficients are introduced. For arbitrary degrees p and q, such differential p-forms and q-vector fields are seen to be the solutions to two second-order partial differential systems on J(2)(M, R-n), which are reducible to two first-order partial differential systems by adding variables. Computational aspects in solving these systems are discussed and examples and applications are also given. Read More
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