Geodesic
Derivational equations of submanifolds in an asymmetric affine connection space
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 265

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In a space $L_N$ of asymmetric affine connection one observes a submanifold, defined in local coordinates. Because of the asymmetry of the connection in the space, the connection of submanifolds is generally asymmetric. Based on this, it follows that 4 kinds of covariant derivatives and 4 kinds of derivational equations are possible. In the present paper is proved that by applying the $3^{rd}$, or the $4^{th}$ kind of covariant derivative, it follows that the induced connection is symmetric (Theorem 1.2.). In the pseudonormal submanifold are defined 2 connections (2.4) and 4 kinds of covariant derivative. It is proved that by applying the $3^{rd}$ or the $4^{th}$ kind of derivative one concludes that the induced connections in this case is unique (Theorem 2.2). In $\S 3$ are examined some properties of coefficients of derivational equations and induced connection in pseudonormal subspace.
Classification : 53C25 53A45 53B05
Keywords: Derivational equations, Submanifold, Space with asymmetric affine connection, Induced connection, Pseudonormal submanifold 
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     author = {Svetislav M. Min\v{c}i\'c},
     title = {Derivational equations of submanifolds in an asymmetric affine connection space},
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Svetislav M. Minčić. Derivational equations of submanifolds in an asymmetric affine connection space. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 265 . http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a5/