Tanveer Fatima | Searcharxiv

arXiv2026

Casorati inequalities along vertical and horizontal distributions of pointwise slant riemannian submersions

We establish optimal Casorati inequalities for pointwise slant Riemannian submersions. As such a submersion carries two distinct distributions, the vertical, tangent to the fibers, and the horizontal, governed by O'Neill's tensors T and A, we treat them separately. For submersions from generalized complex and generalized Sasakian space forms we bound the normalized scalar curvature of each distribution by its normalized Casorati curvatures. Special cases recover sharp inequalities for real, complex, K\"ahler, Sasakian, Kenmotsu, cosymplectic, and almost and almost space forms. Equality is characterized geometrically: invariantly quasi-umbilical fibers in the vertical case and integrability in the horizontal case. The invariant and anti-invariant limits reproduce known results, and examples illustrate sharpness.

math.DG↗

arXiv2021

Almost Yamabe Solitons on a Total Space of Almost Hermitian Submersions

This article presents the study of almost Hermitian submersion from an almost Yamabe soliton onto an almost Hermitian manifold. A non-trivial example is also mentioned in order to guarantee the existence of such solitons on the total space of almost Hermitian submersions. We mainly focus on Kaehler submersions from Kaehler manifolds which are special case of almost Hermitian submersions. Under certain conditions, we find out that the fibres and the base manifold of such submersions are almost Yamabe soliton. We give the characterizations for an almost Yamabe soliton of a Kaehler submersion to be shrinking, steady and expanding in terms of extrinsic horizontal scalar curvature. Moreover, we observe the behavior of torqued, recurrent and concurrent vector field of the total space of the Kaehler submersion. In particular, we obtain characterization for an almost Yamabe soliton consisting of concurrent vector fields. Meanwhile, we give some results of such submersions when the total space is Yamabe soliton which is a particular case of almost Yamabe soliton.

math.DG↗