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Let (M,g) be a pseudo-Riemannian manifold and $T^2M$ be its the second-ordertangent bundle equipped with the deformed 2-nd lift metric g which obtainedfrom the 2-nd lift metric by deforming the horizontal part with a symmetric(0,2)-tensor field c. In the present paper, we first compute the Levi-Civitaconnection and its Riemannian curvature tensor field of $(T^2M,g)$. We givenecessary and sufficient conditions for $(T^2M,g)$ to be semi-symmetric.Secondly, we show that $(T^2M,g)$ is a plural-holomorphic B-manifold with thenatural integrable nilpotent structure. Finally, we get the conditions underwhich $(T^2M,g)$ with the 2-nd lift of an almost complex structure is ananti-K\"ahler manifold

On the second-order tangent bundle with deformed 2-nd lift metric