Almost f-Cosymplectic Manifolds

Notes on Ricci Solitons in f-Cosymplectic Manifolds

“…On the other hand, as in [1], it easily follows ω = 1 e 2θ(z) dx ∧ dy and dω = −2θ ′ (z)e −2θ(z) dx ∧ dy ∧ dz = 2θ ′ (z)ω ∧ η.…”

“…Later Kim and Pak in [12] defined a new class called as almost α-cosymplectic manifolds by combining almost cosymplectic and almost α-Kenmotsu manifolds, where α is a real number. Recently, Based on Kim and Pak's work, Aktan et al [1] considered a wide subclass of almost contact manifolds, which are called almost f -cosymplectic manifolds defined by choosing a smooth function f in the conception of almost α-cosymplectic manifolds instead of any real number α.…”

Ricci solitons in almost $f$-cosymplectic manifolds

“…In particular, M is an almost cosymplectic manifold if α = 0 and an almost Kenmotsu manifold if α = 1. In [1], a class of more general almost contact manifolds was defined by generalizing the real number α to a smooth function f . More precisely, an almost contact metric manifold is called an almost f -cosymplectic manifold if dη = 0 and dω = 2f η ∧ ω are satisfied, where f is a smooth function with df ∧ η = 0.…”

“…Let M be an almost f -cosymplectic manifold, we recall that there is an operator h = 1 2 L ξ φ which is a self-dual operator. The Levi-Civita connection is given by (see [1])…”

Quasi-Einstein structures and almost cosymplectic manifolds

“…We say that (1,1)-type tensor field φh on (M, g) is said to be an η-parallel tensor if it satisfies the equation g((∇ X φh)Y, Z) = 0 for all tangent vectors X, Y, Z orthogonal to ξ (see [1]). Putting Y = e in (4.31) and using the pervious equations, we obtain…”