We show that the Dirac operator on a spin manifold does not admit L eigenspinors provided the metric has a certain asymptotic behaviour and is a warped product near infinity. These conditions on the metric are fulfilled in particular if the manifold is complete and carries a non-complete vector field which outside a compact set is gradient conformal and non-vanishing.

Abstract A world-volume model of a non-critical 3-brane is quantized in a strong coupling phase in which fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at very high energies far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode non-perturbatively, whil...

We review some material connecting gravity and the quantum potential and provide a few new observations. The main theme is that in utilizing a conformal (Weyl) geometry the metric plus the Weyl vector plus the quantummass field determine spacetime geometry. There are strong connections to deBroglie-Bohm style ideas in quantum theory.

We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of axisymmetry, we have written a program to solve the resulting nonlinear elliptic equation. We have obtained solutions, both numerically and from a linearized ...

A world-volume model of non-critical 3-brane is quantized in a strong coupling phase where fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at the very high energy far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode non-perturbatively, while the tracel...

The purpose of this article is to study implications a Ricci soliton warped product manifold its base and fiber manifolds. First, it proved that if then factors are soliton. Then we on manifolds admitting either conformal vector field or concurrent field. Finally, some space-times.

Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in con-formally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, ...

This research article endeavors to discuss the attributes of Riemannian submersions under canonical variation in terms conformal ?-Ricci soliton and gradient with a potential vector field ?. Additionally, we estimate various conditions for which target manifold submersion is Killing ?(Ric)-vector field. Moreover, deduce generalized Liouville equation satisfying by last multiplier ? vertical ? s...

Physicists have developed very advanced methods to compute such integrals. For example, the famous Feynman diagram technique allows us to compute the above integral for a rather particular function S(x), a small perturbation of a positive de nite quadratic form in R . Sometimes, elaborate techniques of physicists to compute simple things nd an amazing application to very general things in mathe...