Studies on Santilli's Locally Anisotropic and Inhomogeneous Isogeometries: I. Isobundles and Generalized Isofinsler Geometry

We generalize the geometry of Santilli's locally anisotropic and inhomogeneous isospaces to the geometry of vector isobundles provided with nonlinear and distinguished isoconnections and isometric structures. We present, apparently for the first time, the isotopies of Lagrange, Finsler and Kaluza-Klein spaces. We also continue the study of the interior, locally anisotropic and inhomogeneous gravitation by extending the isoriemannian space's constructions and presenting a geometric background for the theory of isofield interactions in generalized isolagrange and isofinsler spaces.