Ricci decomposition

About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.

The expansion of physical quantities in terms of the irreducible representations of the scale-Euclidean group and applications to the construction of scale-invariant correlation functions

Abstract: The irreducible representations of the scale-Euclidean group in three dimensions are introduced, and the general tensor is expanded in terms of these representations. The cases of zero-rank tensor (scalar), rank-1 tensor (vector), and rank-2 tensor are studied in detail. The expansion is shown to be a generalization of the Helmholtz expansion of a vector into rotational and irrotational parts.

From Infinitesimal Harmonic Transformations to Ricci Solitons

Abstract: The concept of the Ricci soliton was introduced by Hamilton. Ricci soliton is defined by vector field and it's a natural generalization of Einstein metric. We have shown earlier that the vector field of Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.

Pseudolocality of the Ricci Flow Under Integral Bound of Curvature

Abstract: We prove a pseudolocality type theorem for compact Ricci flows under local integral bounds on curvature. The main tool we use here is the local Ricci flow introduced by Deane Yang and the pseudolocality theorem due to Perelman. We also prove a theorem on the extension of the local Ricci flow.

The structure of the Ricci tensor on locally homogeneous Lorentzian gradient Ricci solitons

Abstract: We describe the structure of the Ricci tensor on a locally homogeneous Lorentzian gradient Ricci soliton. In the non-steady case, we show the soliton is rigid in dimensions three and four. In the steady case, we give a complete classification in dimension three.