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...

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: ~1! the shift in the equilibrium geometry ~known as nuclear relaxation!, and ~2! the change in the shape of the potential energy surface ~known as curvature!. Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the e...

Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism are derived, and variations of a generic set of higher-order curvature terms appearing in string effective actions are studied. It is sho...

Scalar field cosmology in three-dimensions. Abstract We study an analytical solution to the Einstein's equations in 2 + 1-dimensions. The space-time is dynamical and has a line symmetry. The matter content is a minimally coupled, massless, scalar field. Depending on the value of certain parameters, this solution represents three distinct space-times. The first one is flat space-time. Then, we h...

We study the intermittency and field-line structure of the MHD turbulence in plasmas with very large magnetic Prandtl numbers. In this regime, which is realized in the interstellar medium, accretion disks, and protogalaxies, magnetic fluctuations can be excited at scales below the viscous cutoff. The salient feature of the resulting small-scale magnetic turbulence is the folded structure of the...