Recently a class of alternative theories of gravity which goes under the name f(R) gravity, has received considerable attention, mainly due to its interesting applications in cosmology. However, the phenomenology of such theories is not only relevant to cosmological scales, especially when it is treated within the framework of the so called Palatini variation, an independent variation with resp...

We develop the basic elements of a Cauchy theory on the complex Levi-Civita field, which constitutes the smallest algebraically closed nonArchimedean extension of the complex numbers. We introduce a concept of analyticity based on differentiation, and show that it leads to local expandability in power series. We show that analytic functions can be integrated over suitable piecewise smooths path...

The Levi-Civita (LC) solution is matched to a cylindrical shell of an anisotropic uid. The uid satis es the energy conditions when the mass parameter is in the range 0 1. The mass per unit length of the shell is given explicitly in terms of , which has a nite maximum. The relevance of the results to the non-existence of horizons in the LC solution and to gauge cosmic strings is pointed out. PAC...

Abstract We study Hessian estimators for functions defined over an $n$-dimensional complete analytic Riemannian manifold. introduce new stochastic zeroth-order using $O (1)$ function evaluations. show that, real-valued $f$, our estimator achieves a bias bound of order $ O ( \gamma \delta ^2 ) $, where depends on both the Levi–Civita connection and $\delta is finite difference step size. To best...

We construct a Connes spectral triple or `Dirac operator' on the non-reduced fuzzy sphere $C_\lambda[S^2]$ as realised using quantum Riemannian geometry with central metric $g$ of Euclidean signature and its associated Levi-Civita connection. The Dirac operator is characterised uniquely up to unitary equivalence within our geometric setting an assumption that spinor bundle trivial rank 2 basis....

The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space-time is obtained. The region of validity of the FaddeevPopov-DeWitt functional is studied. It is shown that the invariant content of general relativity as a constrained system can be covered by two ”equivalent” unconstrained systems: the ”dynamic” (with ”d...

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, post-Minkowskia...

As mentioned in the accompanying biography, Levi-Civita and his teacher Ricci,1 prompted by Felix Klein, wrote an important review of tensor calculus (under the name of ‘absolute differential calculus’) in 1901 [1]. Einstein, advised by Marcel Grossmann, began to study this in 1912 and corresponded with Levi-Civita about it in the period leading up to the publication of the first paper on gener...

Analogous to the characterisation of Brownian motion on a Riemannian manifold as development Euclidean space, we construct sub-Riemannian diffusions equinilpotentisable manifolds by developing canonical stochastic process arising lift an associated model space. The notion introduce for uses Cartan connections, which take place Levi-Civita connection in geometry. We first derive general expressi...

In this note we discuss conditions under which a linear connection on a manifold equipped with both a symmetric (Riemannian) and a skew-symmetric (almost-symplectic or Poisson) tensor field will preserve both structures. If (M, g) is a (pseudo-)Riemannian manifold, then classical results due to T. Levi-Civita, H. Weyl and E. Cartan [7] show that for any (1, 2) tensor field T i jk which is skew-...