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3rd order differential invariants of coframes. (English) Zbl 0962.53012
The $$r$$-th order coframe bundle on an $$n$$-dimensional manifold $$X$$ is the space of all invertible $$r$$-jets from $$X$$ into $$\mathbb R^n$$ with target $$0\in \mathbb R^n$$. The authors deduce explicit formulae for a basis of third order invariants of coframes with values in left $$L^i_n$$-manifolds, where $$L^i_n$$ is the $$i$$-th jet group in dimension $$i$$=1,2,3.
##### MSC:
 53A55 Differential invariants (local theory), geometric objects 58A20 Jets in global analysis
##### Keywords:
differential invariant; differential group; frame; coframe
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##### References:
 [1] CHAO, DAO QUI: 2nd Order Differential Invariants on the Bundle of Frames. CSc (=P\?D) Dissertation, Masaryk Univ., Brno (Czech Republic), 1991. [2] DIEUDONNÉ J.: Treatise on Analysis, Vol. III. Academic Press, New York-London, 1972. · Zbl 0268.58001 [3] GARCIA PÉREZ P. L.-MASQUE J. M.: Differential invariants on the bundles of linear frames. J. Georn. Phys. 7 (1990), 395-418. · Zbl 0764.53017 [4] KOLÁŘ I.: On the prolongations of geometric object fields. An. Ştiinţ. Univ. ”Al. I. Cuza” Iaşi Secţ. I a Mat. 17 (1971), 437-446. · Zbl 0366.53037 [5] KOLÁŘ I.-MICHOR P.-SLOVÁK J.: Natural Operations in Differential Geometry. Springer-Verlag, Berlin, 1993. · Zbl 0782.53013 [6] KRUPKA D.: A setting for generally invariant Lagrangian structures in tensor bundles. Bull. Acad. Polon. Sci. Sér. Math. Astr. Phys. 22 (1974), 967-972. · Zbl 0305.58002 [7] KRUPKA D.: Elementary theory of differential invariants. Arch. Math. (Brno) 14 (1978), 207-214. · Zbl 0428.58002 [8] KRUPKA D.: Local invariants of a linear connection. Differential Geometry, Budapest (Hungary), 1979. Colloq. Math. Soc. János Bolyai 31, North Holland, Amsterdam, 1982, pp. 349-369. · Zbl 0513.53038 [9] KRUPKA D.-JANYŠKA J.: Lectures on Differential Invariants. Brno University, Brno (Czech Republic), 1990. · Zbl 0752.53004 [10] KRUPKA D.-MIKOLÁŠOVÁ V.: On the uniqueness of some differential invariants: $$d,\, [\, ,\, ],\, \bigtriangledown$$. Czechoslovak Math. J. 34 (1984), 588-597. · Zbl 0571.53009 [11] KRUPKA M.: Natural Operators on Vector Fields and Vector Distributions. Doctoral Dissertation, Masaryk University, Brno (Czech Republic), 1995. [12] KRUPKA M.: Anti-holonomic jets and the Lie bracket. Arch. Math. (Brno) 34 (1998), 311 319. · Zbl 0915.58005 [13] NIJENHUIS A.: Natural bundles and their general properties. Differential Geometry (In honor of K. Yano), Kinokuniya, Tokyo, 1972, pp. 317-334. · Zbl 0246.53018 [14] THOMAS T. Y.: The Differential Invariants of Generalized Spaces. Cambridge University Press, Cambridge, 1934. · Zbl 0009.08503 [15] WEYL H.: The Classical Groups. Princeton University Press, Princeton, NJ, 1946. · Zbl 1024.20502
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