Semi-invariant submersions whose total manifolds are locally product Riemannian

Some remarks on Riemannian submersions admitting an almost Yamabe soliton

“…Gray [10] and B. O'Neill [11], independently. They presented some fundamental properties and formulas for Riemannian submersions and recently, such a theory has been intensively studied (we refer to [12][13][14][15]).…”

Bi-slant $\xi^{\perp}$-Riemannian submersions

“…Many interesting studies on several types of submersions have been done. For instance, slant and semi-slant submersions [3,[13][14][15][16]21], bi-slant submersions [23], quasi bi-slant submersions [22], anti-invariant Riemannian submersions [25,28], semiinvariant submersions [20,26], pointwise slant submersions [6,18], hemi-slant submersions [30], Lagrangian submersions [29], generic submersions [24].…”

Clairaut Submersion

“…Later, the notion of anti-invariant submersions and Lagrangian submersion from almost Hermitian manifolds onto Riemannian manifolds were introduced by Sahin [4] and studied by Taştan [5,6], Gündüzalp [7], Beri et al [8], Ali and Fatima [9], in which the fibers of submersion are antiinvariant with respect to the almost complex structure of total manifold. After that several new types of Riemannian submersions were defined and studied such as semi-invariant submersion [10,11], slant submersion [12,13], generic submersion [14][15][16][17], hemi-slant submersion [18], semi-slant submersion [19], pointwise slant submersion [20][21][22] and conformal semi-slant submersion [23]. Also, these kinds of submersions were considered in different kinds of structures such as nearly Kähler, Kähler, almost product, para-contact, Sasakian, Kenmotsu, cosymplectic and etc.…”