We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different choices of cross-section.
Bibliographical noteFunding Information:
Thanks to Irina Kogan for many helpful remarks and the referees for useful suggestions. G. G?n Polat acknowledges the support and hospitality during her stay at the University of Minnesota, where this work was initiated.The work of G. G?n Polat is supported by the Scientific and Technological Research Council of Turkey (TUBITAK). The work of P. J. Olver was partially supported by NSF grant DMS-1108894.
© 2019 European Mathematical Society.
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- Binary form
- Classical invariant theory
- Differential invariant
- Joint differential invariant
- Joint invariant
- Moving frame
- Ternary form