4D Einstein equations in a general gauge Kaluza–Klein space

Abstract

Using the new approach on higher-dimensional Kaluza-Klein theories developed by the first author, we obtain the 4D Einstein equations on a (4 + n)D relativistic gauge Kaluza-Klein space. Adapted frame and coframe fields, adapted tensor fields, and the Riemannian adapted connection, have a fundamental role in the study. The high level of generality of the study, enables us to recover several results from earlier papers on this matter.

Обобщенный Тензор Кривизны Вагнера Почти Контактных Метрических Пространств

“…N-продолженные связности естественным образом возникают в различных разделах математики и теоретической физики [13][14][15]. Так, например, в работе [13] с помощью Nпродолженной симплектической связности определяются обобщенные классы Маслова лежандровых подмногообразий почти контактных метрических пространств.…”

(Pseudo) generalized Kaluza–Klein G-spaces and Einstein equations

“…In particular, if (ρ, η, h) = (Id T M , Id M , id M ) and the Lie bracket [, ] T M is the usual Lie bracket, then the formulas of Ricci type (7) and ( 8) reduce to…”

“…Cosmological solutions in which both the cylinder condition and the compactification condition were removed are presented in [9,15,17,18]. An excelent survey on STM theory is presented in the paper of Overduin and Wesson [16].The idea to construct exact solutions with Lie and Clifford algebroid symmetries in modified and extra dimension gravity and matter field theories was elaborated originally in a series of preprints by S. Vacaru [21,22,23]; see further developments and reviews of results on nonholonomic algebroids and Einstein-Direact structures, Finsler-Lagrange-Hamilton algebroid spaces and geometric flows on Lie algebroid in [24,25,26].Recently, Bejancu developed a new point of view on a general Kaluza-Klein theory using the product manifold M = M × K, where M is a four-dimensional manifold and K is a one-dimensional manifold [5,6,7]. The tangent bundle of M is the space used to develop the theory as a direct sum between the horizontal distribution HM and vertical distribution V M .…”

“…Recently, Bejancu developed a new point of view on a general Kaluza-Klein theory using the product manifold M = M × K, where M is a four-dimensional manifold and K is a one-dimensional manifold [5,6,7]. The tangent bundle of M is the space used to develop the theory as a direct sum between the horizontal distribution HM and vertical distribution V M .…”