Abstract
In this chapter we first recall the concept of a geometrical space structure that may be defined on a manifold M once we introduce different metrical fields and different connections on it. Then, we brielfly recall the concepts of curvature, torsion and nonmetricity of a general connection1 on M. Next we recall the concepts of flat space and affine spaces. After that, we explain with details and many examples2 the crucial difference between the concept of curvature of a connection defined on M and the fact that M can eventually be a bent hypersurface in an Euclidean (or pseudo-Euclidean) space with an appropriate number of dimensions. After that, we present the main reason for the proposal of our theory, namely the fact that in Einstein’s General Relativity Theory (GRT) there are no trustworth energy-momentum and angular momentum conservation laws3. At the end of the chapter, we describe the contents of the other chapters and appendices briefly.
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Fernández, V.V., Rodrigues, W.A. (2010). Introduction. In: Gravitation as a Plastic Distortion of the Lorentz Vacuum. Fundamental Theories of Physics, vol 168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13589-7_1
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