A Study on the $\phi$-Symmetric $\mathrm{K}$-Contact Manifold Admitting Quarter-Symmetric Metric Connection

The local $\phi$-symmetry and $\phi$-symmetry of a $\mathrm{K}$-contact manifold with respect to the quarter-symmetric metric connection are studied and the results concerning the $\phi$-symmetry, scalar curvature with respect to the quarter-symmetric and the Levi–Civita connection are obtained. Further, the locally $\mathrm{C}$-Bochner $\phi$-symmetric and the locally $\phi$-symmetric $\mathrm{K}$-contact manifolds with respect to the quarter-symmetric metric connection are studied and some results are obtained. The results are assisted by the examples.