Almost paracontact structures on Kaluza–Klein spaces

Abstract

Kaluza–Klein theory, as a topic of great interest in theoretical physics, applied mathematics and differential geometry, represents the framework in which we develop our study. Based on Bejancu’s results from Bejancu (Prog Theor Phys 128(3):541–585, 2012), we continue here our previous paper Bejan and Chiriac (Int J Geom Methods Mod Phys 10:1, 2013), by dealing with a natural almost paracontact structure on a general Kaluza–Klein space. Such a structure is analogous to the almost contact structure, [see Blair (Contact manifolds in Riemannian geometry. LNM, vol 509. Springer, Berlin, 1976)], which is related to thermodynamics, Mrugala (RIMS Kokyuroku 1142:167–181, 2000), Mrugala (Rep Math Phys 38(3):339–348, 1996). Also, some necessary and sufficient conditions for the existence of Ricci solitons on Kaluza–Klein spaces are provided here.