Abstract:We consider an algebraic representation formula for meromorphic curves in C 3 with preset infinitesimal arc length, i. e., a differential operator M assigning to triples (f, h, d) of meromorphic functions meromorphic curves Φ = (ϕ1, ϕ2, ϕ3) such that d is the infinitesimal arclength of Φ, in this way obtaining the complete solution of the differential equation ϕ Computer algebra systems are an excellent tool to handle formulas of this type. We give simple Mathematica code and apply it to work out some examples… Show more
“…1 This problem was considered in [8], where with the help of quite cumbersome differential-geometric constructions it was shown that system (7) is 3-flat. Our construction, being elementary, allows us to lower the order of the flat control by one.…”
mentioning
confidence: 99%
“…By changing the signature of the quadratic form in Eq. (8), it is possible to obtain a parametrization of the null-curves in pseudo-Euclidean spaces R p,q with min(p, q) > 2. The possible velocity vectors of these curves will cover, however, only some open region in the light cone.…”
We prove that the differential equation for the null-curves of pseudo-Euclidean space R 2,n defines a flat dynamical system in the sense of optimal control theory. The connection with general gauge theories is briefly discussed.
“…1 This problem was considered in [8], where with the help of quite cumbersome differential-geometric constructions it was shown that system (7) is 3-flat. Our construction, being elementary, allows us to lower the order of the flat control by one.…”
mentioning
confidence: 99%
“…By changing the signature of the quadratic form in Eq. (8), it is possible to obtain a parametrization of the null-curves in pseudo-Euclidean spaces R p,q with min(p, q) > 2. The possible velocity vectors of these curves will cover, however, only some open region in the light cone.…”
We prove that the differential equation for the null-curves of pseudo-Euclidean space R 2,n defines a flat dynamical system in the sense of optimal control theory. The connection with general gauge theories is briefly discussed.
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