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The present study initially identified the generalized symmetric connections$(\alpha,\beta)$ typed, which can be regarded as more generalised forms ofquarter and semi-symmetric connections. The quarter and semi-symmetricconnections are obtained respectively particularly when $(\alpha,\beta)=(1,0)$and $(\alpha,\beta)=(0,1)$ are taken into consideration. Taking that intoaccount, a new generalized symmetric metric connection was attained uponKenmotsu manifolds. In compliance with the new connection, some results wereprovided through calculation of tensors belonging to Kenmotsu manifoldinvolving curvature tensor, ricci tensor, projective curvature tensor andcoincircular curvature tensor. Ultimately, an original example was presented.

Some Characterizations in Kenmotsu manifolds with a new connection