Abstract
This paper introduces the concept of an almost quasi-para-Sasakian manifold, which differs from the previously known quasi-para-Sasakian structure in that it is not a normal structure. Instead, it possesses a weaker property called almost normality, similar in properties to integrable tensor structures. Several examples are given, including an almost quasi-para-Sasakian structure defined on the distribution of zero curvature of a sub-Riemanni-an manifold of contact type.
An extended connection with skew-symmetric torsion is defined on an almost quasi-para-Sasakian manifold, which is unique and defined using an intrinsic connection and an endomorphism that preserves the distribution of an almost (para-)contact manifold. The paper proves that the extended connection is a metric connection, and it is also demonstrated that an almost quasi-para-Sasakian manifold can be an n-Einstein manifold with respect to an extended connection with skew-symmetric torsion, provided certain conditions are met.