Geodesic
Special compositions in affinely connected spaces without a torsion
Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 211-220.

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Let AN be an affinely connected space without a torsion. With the help of N independent vector fields and their reciprocal covectors is built an affinor which defines a composition Xn ×Xm (n+m = N). The structure is integrable. New characteristics by the coefficients of the derivative equations are found for special compositions, studied in [1], [3]. Two-dimensional manifolds, named as bridges, which cut the both base manifolds of the composition are introduced. Conditions for the affine deformation tensor of two connections where the composition is simultaneously of the kind (g-g) are found.
Keywords: Affinely Connected Spaces, Spaces of Compositions, Affinor of Composition, Tensor of the Affine Deformation, Integrable Structure, Projective Affinors 
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     title = {Special compositions in affinely connected spaces without a torsion},
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Zlatanov, Georgi. Special compositions in affinely connected spaces without a torsion. Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 211-220. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_3_a1/