H. A. Hayden [1] introduced the idea of semi-symmetric non-metric connection on a Riemannian manifold in (1932). Agashe and Chafle [1] defined and studied semi-symmetric non-metric connection on a Riemannian manifold. In the present paper, we define a new type of semi-symmetric non-metric connexion in an almost contact metric manifold and studied its properties. In the end, we have studied some properties of the covariant almost analytic vector field equipped with semisymmetric non-metric connection.2000 Mathematics Subject Classification : 53B15.

This article deals with the investigation of perfect fluid GRW spacetimes. It is shown that in a GRW perfect fluid spacetime, the Weyl tensor is divergence free and in dimension 4, a perfect fluid GRW spacetime is a RW spacetime. Moreover, we prove that if a GRW perfect fluid spacetime admits a second order symmetric parallel tensor, then either the state equation of the perfect fluid GRW spacetime is characterized by p = 3−n n−1 µ , or the tensor is a constant multiple of the metric tensor. We also characterize the perfect fluid GRW spacetimes whose Lorentzian metrics are Ricci soliton, gradient Ricci soliton, gradient Yamabe solitons and gradient m-quasi Einstein solitons, respectively.

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The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change. Moreover, we have deduced the expression of Ricci curvature for the aforementioned space with vanishing the S-curvature. These findings contribute significantly to understanding the complex nature of Finsler spaces and their curvature properties.

We characterize almost co-Kähler manifolds with gradient Yamabe, gradient Einstein and quasi-Yamabe solitons. It is proved that if the metric of a [Formula: see text]-almost co-Kähler manifold [Formula: see text] is a gradient Yamabe soliton, then [Formula: see text] is either [Formula: see text]-almost co-Kähler or [Formula: see text]-almost co-Kähler or the metric of [Formula: see text] is a trivial gradient Yamabe soliton. A [Formula: see text]-almost co-Kähler manifold with gradient Einstein soliton is [Formula: see text]-almost co-Kähler. Finally, it is shown that an almost co-Kähler manifold admitting a quasi-Yamabe soliton, whose soliton vector is pointwise collinear with the Reeb vector field of the manifold, is [Formula: see text]-almost co-Kähler. Consequently, some results of almost co-Kähler manifolds are deduced.