We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies (i) concircular field equation and compact, (ii) special equation. Finally, we that, complete connected admits non-isometric vector leaving invariant, conformal function concircular, then constant.

Using the visual search method, we show that stimuli that contain curvature discontinuities (i.e., points where the second derivative along an image contour is not defined) are easily found among stimuli containing only smooth changes in curvature. Curved stimuli that lack curvature discontinuities, however, are difficult to find among distractors that have them. These results suggest that the ...

We consider a self-interacting scalar field theory in a slowly varying gravitational background field. Using zeta-function regularization and heat-kernel techniques, we derive the one-loop effective Lagrangian up to second order in the variation of the background field and up to quadratic terms in the curvature tensors. Specializing to different spacetimes of physical interest, the influence of...

Considering Joule heating caused by the dissipation of the magnetic field in the neutron star crust to be an efficient mechanism in maintaining a relatively high surface temperature in very old neutron stars, the role of general relativity is investigated. It is found that, although the effect of space-time curvature produced by the intense gravitational field of the star slows down the decay r...

There are many inflationary models in which inflaton field does not satisfy the slow-roll condition. In such models, it is difficult to generate the curvature perturbation during inflation. Thus, to generate the curvature perturbation, one must introduce another component to the theory. To cite a case, curvatons may generate dominant part of the curvature perturbation after inflation. However, ...

A continuum mechanical model based on the Helfrich Hamiltonian is devised to investigate the coupling between lipid composition andmembrane curvature. Eachmonolayer in the bilayer is modeled as a freely deformable surface with a director field for lipid orientation. A scalar field for the mole fraction of two lipid types accounts for local changes in composition. It allows lipids to access mono...

The self-consistent system of master equations describing the kinetics of a relativistic non-Abelian plasma, influenced by curvature interactions, is formulated. Non-minimal (curvature induced) coupling is shown to modify all the subsystems of the model: the gauge field equations, the gravity field equations and the kinetic equation for colored particles.

The energy of the stochastic magnetic field is bounded from below by a topological quantity expressing the degree of linkage of the field lines. When the bound is saturated one can assume that the storage of a certain magnetic energy requires a minimal degree of topologi-cal complexity. It is then possible to infer a connection between the helicity content and the average curvature of the magne...