Topics in Gravitation and Electromagnetism

On tangent geometry and generalised continuum with defects

“…One of the possible reasons is that this theory is constructed on a restrictive geometrical formulation. The present paper is a contribution in this direction among recent works [22, 38–40].…”

“…As has been underlined previously, connection having both torsion and curvature cannot be obtained with single-valued tetrads. Another method consists of introducing an additional gauge field to give a connection [70] (see the discussion in [22]):…”

“…RC manifold This appendix is a review of basic contents concerning RC geometry. All details can be found in the standard textbooks [22, 51, 52, 72]. On a manifold B , one considers a metric tensor g , its tangent space T B and its space X ( B ) of C ∞ vector fields. Definition A.1 (Covariant derivative).…”

“…This appendix is a review of basic contents concerning RC geometry. All details can be found in the standard textbooks [22, 51, 52, 72].…”

“…Another well-known approach consists of focusing on the discontinuity of scalar and vectorial fields [15] by invoking multivalued fields [21]. Such an approach is a microscopic alternative interpretation of the non-holonomy supported by geometrical quantities (scalar or tensorial) at a scale for which the material may be interpreted as a continuum [22]. Even if this approach was inspired by the elastoplastic transformation of crystals, its applications have a wider range including relativity and quantum mechanics [13, 23].…”