LIGHTLIKE HYPERSURFACES OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH AN (ℓ, m)-TYPE CONNECTION

LIGHTLIKE HYPERSURFACES OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH AN (ℓ, m)-TYPE CONNECTION

We define a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. We say that this connection is an (${\ell}$, m)-type connection. Semi-symmetric non-metric connection and non-metric ${\phi}$-symmetric connection are two important examples of this connection such that (${\ell}$, m) = (1, 0) and (${\ell}$, m) = (0, 1), respectively. In this paper, we study lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (${\ell}$, m)-type connection.

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