Search results for "Covariant derivative"
showing 7 items of 7 documents
The role of virtual work in Levi-Civita's parallel transport
2015
The current literature on history of science reports that Levi-Civita’s parallel transport was motivated by his attempt to provide the covariant derivative of the absolute differential calculus with a geometrical interpretation (For instance, see Scholz in The intersection of history and mathematics, Birkhauser, Basel, pp 203–230, 1994, Sect. 4). Levi-Civita’s memoir on the subject was explicitly aimed at simplifying the geometrical computation of the curvature of a Riemannian manifold. In the present paper, we wish to point out the possible role implicitly played by the principle of virtual work in Levi-Civita’s conceptual reasoning to formulate parallel transport.
A short proof of a theorem of Ahlfors
1988
In [1] Ahlfors proved that the Weil-Petersson metric of the Teichmfiller space is K~hler. A new proof was given by Fischer and Tromba [5] in a purely Riemannian setting of Teichmfiller theory [3]. We shall provide yet another proof that slightly shortens the argument of Fischer and Tromba. We begin with a brief review of the Fischer-Tromba approach to Teichmiiller theory [3-5]. Let M be a compact connected oriented 2-dimensional manifold without boundary.
Systematic study of octet-baryon electromagnetic form factors in covariant chiral perturbation theory
2017
We perform a complete and systematic calculation of the octet-baryon form factors within the fully covariant approach of SU(3) chiral perturbation theory at O(p^3). We use the extended on-mass shell renormalization scheme, and include explicitly the vector mesons and the spin-3/2 decuplet intermediate states. Comparing these predictions with data including magnetic moments, charges, and magnetic radii, we determine the unknown low-energy constants, and give predictions for yet unmeasured observables, such as the magnetic moment of the Sigma^0, and the charge and magnetic radii of the hyperons.
Generalized curvature and the equations of D=11 supergravity
2005
It is known that, for zero fermionic sector, the bosonic equations of Cremmer-Julia-Scherk eleven-dimensional supergravity can be collected in a compact expression which is a condition on the curvature of the generalized connection. Here we peresent the equation which collects all the bosonic equations of D=11 supergravity when the gravitino is nonvanishing.
Geometrical foundations of fractional supersymmetry
1997
A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a $q$-deformed boson. The limit of this algebra when $q$ is a $n$-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge $Q$ and covariant derivative $D$ encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Berezin integral and fractional superspace measure arise as a natural part of our formalism. When $q$…
L-Rigidity in Newtonian approximation
2008
Newtonian limit of L-Rigidity is obtained. In this formalism, L-Rigidity is reduced to steady Newtonian rigid motions in a Newtonian frame of reference in which the observer is at rest.
Spacelike energy of timelike unit vector fields on a Lorentzian manifold
2004
On a Lorentzian manifold, we define a new functional on the space of unit timelike vector fields given by the L2 norm of the restriction of the covariant derivative of the vector field to its orthogonal complement. This spacelike energy is related with the energy of the vector field as a map on the tangent bundle endowed with the Kaluza–Klein metric, but it is more adapted to the situation. We compute the first and second variation of the functional and we exhibit several examples of critical points on cosmological models as generalized Robertson–Walker spaces and Godel universe, on Einstein and contact manifolds and on Lorentzian Berger’s spheres. For these critical points we have also stu…