‎the object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎at first we prove that a quasi-conformally flat spacetime is einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎einstein's field equation with cosmological constant is covariant constant‎. ‎next‎, ‎we prove that if the perfect...

The induced Einstein equation on a perturbed brane in the Induced Matter Theory is reanalyzed. We indicate that in a conformally flat background, the local quantum corrections to the Einstein equation can be obtained via the IMT. Using the FRW metric as the 4D gravitational model, we show that the classical fluctuations of the brane may be related to the quantum corrections to the classical Ein...

the overall aim of this study is to calculate some water properties in the single wall carbon naotubes (swcnt) and compare them to the bulk water properties to investigate the deviation of water properties inside the swcnt from those in the bulk. here some physical and transport properties of water molecules in the single wall carbon nanotube were reported by performing molecular dynamics (md) ...

We define an elliptic equation for Hermitian metrics which is related to the Einstein condition. Solutions to this equation are closely related to Kähler-Einstein metrics, and are automatically Kähler-Einstein when a certain non-positive condition is satisfied by c1(M). Given this, a natural flow equation arises taking Hermitian metrics to Kähler metrics. We prove short time existence and regul...

We define an elliptic equation for Hermitian metrics which is related to the Einstein condition. Solutions to this equation are closely related to Kähler-Einstein metrics, and are automatically Kähler-Einstein when a certain non-positive condition is satisfied by c1(M). Given this, a natural flow equation arises taking Hermitian metrics to Kähler metrics. We prove short time existence and regul...

We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler-Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler-Einstein metrics, and are automatically Kähler-Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existen...

A closed Riemannian manifold (Mn, g) is called Einstein if the Ricci tensor of g is a multiple of itself; that is, ric(g) = λ · g. This equation, called the Einstein equation, is a complicated system of second order partial differential equations, and at the present time no general existence results for Einstein metrics are known. However, there are results for many interesting classes of Einst...

The Boyer-Finley equation, or SU(∞)-Toda equation is both a reduction of the self-dual Einstein equations and the dispersionless limit of the 2d-Toda lattice equation. This suggests that there should be a dispersive version of the self-dual Einstein equation which both contains the Toda lattice equation and whose dispersionless limit is the familiar self-dual Einstein equation. Such a system is...