Conformal generic submersions

Generic Submersions in Contact Geometry

“…In this section we define and study the concept of generic submersion from an almost contact metric manifold onto a Riemannian manifold. We would like to mention that there are other notions of generic submanifolds, [12,13,14].…”

“…If the Reeb vector field ξ is tangent to 𝑘𝑒𝑟π * , then 𝐷 0 ∩ 𝑘𝑒𝑟𝑄 = 𝑠𝑝𝑎𝑛{ξ}. Consider a pair of almost complex structures {𝐽 1 , 𝐽 2 } on 𝑅12 as in the following:𝐽 1 (∂ 1 , … ∂ 12 ) = (− ∂ 3 , − ∂ 4 , ∂ 1 , ∂ 2 , − ∂ 7 , − ∂ 8 , ∂ 5 , ∂ 6 , − ∂ 11 , − ∂ 12 , ∂ 9 , ∂ 10 ), 𝐽 2 (∂ 1 , … , ∂ 12 ) = (− ∂ 2 , ∂ 1 , ∂ 4 , − ∂ 3 , − ∂ 6 , ∂ 5 , ∂ 8 , − ∂ 7 , − ∂ 10 , ∂ 9 , ∂ 12 , − ∂ 11 )Define a map π: 𝑅 𝟙𝟛 → 𝑅 𝟞 such that π(𝑥 1 , … , 𝑥 13 ) = (𝑥 2 , 𝑥 3 , 𝑥 6 , 𝑥 8 , 𝑥 9 , 𝑥 12 ).…”

Pseudo‐projective and quasi‐conformal curvature tensors on Riemannian submersions

“…1 Later, many studies have been done on the theory of Riemannian submersions. [2][3][4] However, the study of curvature tensors on Riemannian submersions has emerged very recently.…”

“…B.O'Neill developed several fundamental equations and curvature relations among the total space, the base space and the fibers on a submersion in 1966 1 . Later, many studies have been done on the theory of Riemannian submersions 2–4 . However, the study of curvature tensors on Riemannian submersions has emerged very recently.…”