The idea of this research is to study different types of connections in an almost Hermite manifold. The connection has been established between linear connection and Riemannian connection. Three new linear connections ∇1, ∇2, ∇3 are introduced. The necessary and sufficient condition for ∇1, ∇2, ∇3 to be metric is discussed. A new metric s* (X,Y) has been defined for (Mn,F,g*) and additional properties are discussed. It is also proved that for the quarter symmetric connection ∇ is unique in given manifold. The hessian operator with respect to all connections defined above has also been discussed.
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