Kaluza-Klein theory with scalar fields and generalised Hopf manifolds

Abstract

The authors consider the spontaneous compactification induced by a scalar sector in the form of a non-linear sigma model. A very general class of solutions is given by Riemannian submersions from the extra dimensional space onto the space in which the scalar fields take values. An explicit example is constructed taking for the extra dimensional space a generalised Hopf manifold. A massless gauge field is associated with a vertical Killing vector of the Lee type.

Semi-Slant Submersions from Almost Product Riemannian Manifolds

“…Riemannian submersion ( [5], [11]), slant submersion ( [6], [12], [13]), almost Hermitian submersion [16], quaternionic submersion [7], etc. As we know, Riemannian submersions are related with physics and have their applications in the Yang-Mills theory ( [3], [17]), Kaluza-Klein theory ( [2], [8]), semi-invariant submersion( [14]), supergravity and superstring theories ( [9], [10]), etc. In [15], the author studied the slant and semi-slant submanifolds of an almost product Riemannian manifold.…”

H-v-Semi-Slant Submersions From Almost Quaternionic Hermitian Manifolds

“…As we know, Riemannian submersions are related with physics and have their applications in the Yang-Mills theory ( [4], [25]), Kaluza-Klein theory ( [5], [12]), Supergravity and superstring theories ( [13], [15]), etc. And the quaternionic Kähler manifolds have applications in physics as the target spaces for nonlinear σ-models with supersymmetry [7].…”

Pointwise Slant Submersions

“…Riemannian submersions have several applications in mathematical physics. Indeed, Riemannian submersions have their applications in the Yang-Mills theory ( [2,24]), Kaluza-Klein theory ( [3,15]), supergravity and superstring theories ( [16,18]), etc. Later such submersions were considered between manifolds with differentiable structures, see: [11].…”