This is a survey of recent contributions to the area of special Kähler geometry. It is based on lectures given at the 21st Winter School on Geometry and Physics held in Srni in January 2001. 1 Remarkable features of special Kähler manifolds A (pseudo-) Kähler manifold (M,J, g) is a differentiable manifold endowed with a complex structure J and a (pseudo-) Riemannian metric g such that (i) J is ...

For a compact Lie group G we consider lattice gauge model given by the G-Hamiltonian system which consists of cotangent bundle power with its canonical symplectic structure and standard moment map. We explicitly construct Fedosov quantization underlying manifold using Levi–Civita connection Killing metric on G. then explain refine quantized homological reduction for construction star product sy...

Power series with rational exponents on the real numbers field and the Levi-Civita field are studied. We derive a radius of convergence for power series with rational exponents over the field of real numbers that depends on the coefficients and on the density of the exponents in the series. Then we generalize that result and study power series with rational exponents on the Levi-Civita field. A...

We investigate the Cartan formalism in F(R) gravity. gravity has been introduced as a theory to explain cosmologically accelerated expansions by replacing Ricci scalar R Einstein–Hilbert action with function of R. As is well-known, rewritten scalar–tensor using conformal transformation. described based on Riemann–Cartan geometry formulated vierbein-associated local Lorenz symmetry. In formalism...

We consider the metric-affine formulation of bumblebee gravity, derive field equations, and show that connection can be written as Levi-Civita a disformally related metric in which determines disformal part. As consequence, gets coupled to all other matter fields present theory, potentially leading nontrivial phenomenological effects. To explore this issue we compute weak-field limit study resu...

In the following GR9 (1980) Conference abstract, we briefly considered a covariant reformulation of the GR from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a perspective of geometrodynamics, a definition of a reference frame as a differential manifold with an affine connection results in separation of the respective contributions of inertial...

We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resulting system of Euler–Lagrange equations. In the first part of the paper we lo...