In this paper, we classify the four-dimensional gradient shrinking solitons under certain curvature conditions satisfied by all solitons arising from finite-time singularities of Ricci flow on compact four-manifolds with positive isotropic curvature. As a corollary, we generalize a result of Perelman on three-dimensional gradient shrinking solitons to dimension four.

An examination is carried out for three-dimensional incompressible viscoelastic fluid flow over a porous stretching/shrinking sheet with hybrid nanoparticles copper-alumina (Cu−Al2O3) in base water (H2O). The uniform magnetic field of strength B0 applied perpendicular to the and considered Navier slip. mass transfer chemical reaction rate. governing equation defined forms system partial differe...

This paper is devoted to the analysis of heat transfer and Navier’s slip effects in a non-Newtonian Jeffrey fluid flowing past stretching/shrinking sheet. The nanoparticles, namely, Cu Al2O3 are used with water-based Prandtl number 6.272. Velocity flow assumed occur when characteristic size system small or pressure very small. By using similarity transformations, governing nonlinear PDEs turned...