Scalar curvature

About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.

Unification of inflation and cosmic acceleration in the Palatini formalism

Abstract: A modified model of gravity with additional positive and negative powers of the scalar curvature, $R$, in the gravitational action is studied. This is done using the Palatini variational principle. It is demonstrated that using such a model might prove useful to explain both the early time inflation and the late time cosmic acceleration without the need for any form of dark energy.

Analysis for Diffusion Processes on Riemannian Manifolds

Abstract: Diffusion Processes on Riemannian Manifolds Reflecting Diffusion Processes on Riemannian Manifolds with Boundary Coupling and Applications Harnack Inequalities and Applications Functional Inequalities and Applications Formulae for the Curvature and Second Fundamental Form Equivalent Semigroup Inequalities for the Lower Bounds of Curvature and Second Fundamental Form Modified Curvature and Applications Robin Semigroup and Applications Stochastic Analysis on the Path Space Over Manifolds with Boundary Subelliptic Diffusion Processes.

Constant scalar curvature metrics on toric surfaces

Abstract: This paper completes a programme to determine which toric surfaces admit Kahler metrics of constant scalar curvature/

The general form of supersymmetric solutions of N = (1, 0) U(1) and SU(2) gauged supergravities in six dimensions

Abstract: We obtain necessary and sufficient conditions for a supersymmetric field configuration in the N = (1, 0) U(1) or SU(2) gauged supergravities in six dimensions, and impose the field equations on this general ansatz. It is found that any supersymmetric solution is associated with an structure. The structure is characterized by a null Killing vector which induces a natural 2 + 4 split of the six-dimensional spacetime. A suitable combination of the field equations implies that the scalar curvature of the four-dimensional Riemannian part, referred to as the base, obeys a second-order differential equation; surprisingly, for a large class of solutions the equation in the SU(2) theory requires the vanishing of the Weyl anomaly of N = 4 SYM on the base. Bosonic fluxes introduce torsion terms that deform the structure away from a covariantly constant one. The most general structure can be classified into terms of its intrinsic torsion. For a large class of solutions the gauge field strengths admit a simple geometrical interpretation: in the U(1) theory the base is Kahler, and the gauge field strength is the Ricci form; in the SU(2) theory, the gauge field strengths are identified with the curvatures of the left-hand spin bundle of the base. We employ our general ansatz to construct new solutions; we show that the U(1) theory admits a symmetric Cahen–Wallach4 × S2 solution together with a compactifying pp-wave. The SU(2) theory admits a black string, whose near horizon limit is AdS3 × S3, which is supported by a self-dual 3-form flux and a meron on the S3. In the limit of the zero 3-form flux we obtain the Yang–Mills analogue of the Salam–Sezgin solution of the U(1) theory, namely R1,2 × S3. Finally we obtain the additional constraints implied by enhanced supersymmetry, and discuss Penrose limits in the theories.