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In the work [10] we obtained derivational equations of a submanifold of a space LN with asymmetric affine connection. Based on asymmetry of the connection we define four kinds of covariant derivative and obtain four kinds of derivational equations. In [20] are examined integrability conditions of derivational equations, using the 1st and the 2nd kind of derivative, and in the present work we do it on the base of the 3rd and 4th kind. 2010 Mathematics Subject Classification: 53C25; 53A45; 53B05.

New integrability conditions of derivation equations in a subspace of asymmetric affine connection space