A Class of Lorentzian α-Sasakian Manifolds

Abstract

Abstract. In this study we consider φ−conformally flat, φ−conharmonically flat, φ−projectively flat and φ−concircularly flat Lorentzian α−Sasakian manifolds. In all cases, we get the manifold will be an η−Einstein manifold.

$\mathcal{T}$-CURVATURE ON LORENTZIAN $\alpha$-SASAKIAN MANIFOLDS

“…A (2n + 1)-dimensional smooth manifold M is said to be Lorentzian α-Sasakian manifold if it admits a (1, 1)-tensor field φ, a contravariant vector field ξ, global differentiable 1-form η and a Lorentzian metric g which satisfy [15] …”

Quarter-symmetric metric connection on a Lorentzian alpha-Sasakian manifold

“…A n-dimensional differentiable manifold M is called a Lorentzian α-Sasakian manifold [21], if it admits a (1) tensor field ϕ, a contravariant vector field ξ , a covariant vector field η and a Lorentzian metric g which satisfy,…”

“…In 2005, Yildiz and Murathan [21] introduced Lorentzian α-Sasakian manifold. Later, many geometers have studied Lorentzian α-Sasakian manifolds with different curvature restrictions in the papers [1,4,21,22] and others.…”

Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection

“…∀X, Y ∈ χ(M ) and for smooth functions α on M , ∇ denotes the covariant differentiation with respect to Lorentzian metric g ( [9], [17]). …”

“…In 2005, Yildiz and Murathan ( [15]) studied Lorentzian α-Sasakian manifolds and proved that conformally flat and quasi conformally flat Lorentzian α-Sasakian manifolds are locally isometric with a sphere. In 2012, Yadav and Suthar ( [16]) studied Lorentzian α-Sasakian manifolds.…”