The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

This paper proposes a decision treemodel for specifying the importance of 21 factors causing the landslides in a wide area of Penang Island, Malaysia. These factors are vegetation cover, distance from the fault line, slope angle, cross curvature, slope aspect, distance from road, geology, diagonal length, longitude curvature, rugosity, plan curvature, elevation, rain perception, soil texture, s...

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manif...

Abstract In this paper, we consider a dilation type inequality on weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry. We investigate the an isoperimetric by introducing profile and estimate it one for corresponding model space under lower Ricci curvature bounds. also explore functional inequalities derived from comparison of profiles n...

Liquid propane nanobridges were found through molecular dynamics simulations to exhibit in vacuum a symmetric break-up profile shaped as two cones joined in their apexes. With a surrounding gas of sufficiently high pressure, a long-thread profile develops with an asymmetric shape. The emergence of a long-thread profile, discussed previously for macroscopic fluid structures, originates from the ...

The two-field !pressure/density" model for the L→H transition is extended and analyzed qualitatively. In its original form the model is ambiguous as to the location of the transition within the range of bistability of particle and thermal fluxes. Here, the model is regularized by including !i" hyperdiffusion, !ii" time dependence, and !iii" curvature of the pressure profile. The regularizations...