M.A. Akyol and B. Şahin [Conformal anti-invariant Riemannian maps to Kaehler manifolds, U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 4, 2018] defined studied the notion of conformal manifolds. In this paper, as a generalization totally real submanifolds maps, we extend almost contact metric manner, introduce from manifolds cosymplectic order guarantee existence notion, give non-trivial example, i...