Curvature properties of Morris-Thorne wormhole metric

The Morris-Thorne wormhole is a spherically symmetric solution of Einstein field equations with cosmological constant. The present article aims to investigate the geometric properties in terms of curvatures admitted by this spacetime. It is found that such a spacetime possesses several kinds of symmetries, such as, Ricci generalized pseudosymmetry, Ricci generalized projectively pseudosymmetry, pseudosymmetry due to Weyl conformal curvature, semisymmetry due to conharmonic curvature etc. Also, it is an Einstein manifold of level 2 as well as special quasi-Einstein manifold. The Tachibana tensor due to energy momentum tensor of the wormhole satisfies some conditions of pseudosymmetric type and also the energy momentum tensor is Weyl compatible and Riemann compatible. Finally, this spacetime is compared with the Gödel spacetime with respect to their admitting geometric structures.