On fibred Sasakian spaces with vanishing contact Bochner curvature tensor

Statistical manifolds with almost contact structures and its statistical submersions

“…A Riemannian submersion π : M → B is a mapping of M onto B such that π has maximal rank and π * preserves lengths of horizontal vectors ( [5], [6], [11], [17]). If π : M → B is a Riemannian submersion such that M is a Sasakian manifold with almost contact structure (ϕ, ξ, η), each fiber is a ϕ-invariant submanifold of M and tangent to the vector ξ, then π is said to be a Sasakian submersion ( [7], [8], [13], [16]). If π is a Sasakian submersion, then B is Kählerian and each fiber is Sasakian.…”

“…If π is a Sasakian submersion, then B is Kählerian and each fiber is Sasakian. B. H. Kim ([8]) and the author ( [13]) investigated a Sasakian submersion with vanishing contact Bochner curvature tensor. It is known that ( [7], [13] Next, let M and B be two semi-Riemannian manifolds.…”

“…B. H. Kim ([8]) and the author ( [13]) investigated a Sasakian submersion with vanishing contact Bochner curvature tensor. It is known that ( [7], [13] Next, let M and B be two semi-Riemannian manifolds. A semi-Riemannian submersion π : M → B is a submersion such that all fibers are semi-Riemannian submanifolds of M , and π * preserves lengths of horizontal vectors ( [12]).…”

Locally Conformal Almost Cosymplectic Manifold of Φ-holomorphic Sectional Conharmonic Curvature Tensor

“…In 1988, Kim [7] studied total spaces of constant Φ-holomorphic sectional curvature and in 1989, he studied [8] total spaces with flat contact Bochner curvature tensor for fibred Sasakian spaces with conformal fibres. In 1993, Takano [18] discuss fibred Sasakian spaces of constant Φ-holomorphic sectional and at the same time Nagaich [14] showed a generalized Tanno's results for indefinite almost Hermitian manifold. In 2009, Rani et al [17] considered similar condition of [19] to another distinct class of almost contact manifold known as ( )-Sasakian manifold.…”

K"ahlerian submersions with vanishing Bochner curvature tensor

“…On the other hand, Riemannian submersions with almost contact structure of contact structure is studied in [2] and [8]. Also, B. H. Kim [3] and the author [7] have investigated Riemannian subersions with Sasakian structure such that contact Bochner curvature tensor of the total space vanishes identically.…”