On one problem of connections in the space of non-symmetric affine connection and its subspace

Abstract

Let $X_M$ be a submanifold of a differentiable manifold $X_N$
$(X_M\subset X_N)$. If on $X_N$ a non-symmetric affine connection
$L$ is defined by coefficients $ \LL ijk\ne\LL ikj$ and on $X_M$
a non-symmetric basical tensor $g\, (g_{\alpha\beta}\ne
g_{\beta\alpha})$ is given, in the present paper we investigate
the problem: Find a relation between induced connection
$\overline{L}$ from $L_N$ into $X_M$ end the connection
$\overline{\Gamma}$, defined by the tensor $g$ in $X_M$. The
solutions is given in the Theorem 3.1., that is by the equation
(\ref{3.9}). Some examples are constructed.