scholarly journals Some Type I Solutions of Ricci Flow with Rotational Symmetry

2014 ◽  
Vol 2015 (16) ◽  
pp. 7365-7381
Author(s):  
Jian Song
Keyword(s):  
Ricci Flow ◽  
Rotational Symmetry ◽  
Type I

scholarly journals An example of how the Ricci flow can increase topological entropy

2007 ◽  
Vol 27 (6) ◽  
pp. 1919-1932 ◽  
Author(s):  
DAN JANE
Keyword(s):  
Numerical Integration ◽  
Topological Entropy ◽  
Ricci Flow ◽  
Geodesic Flow ◽  
Rotational Symmetry ◽  
Melnikov Method ◽  
Flow Perturbation ◽  
Surface Of Revolution

AbstractWe give a surface for which the Ricci flow applied to the metric will increase the topological entropy of the geodesic flow. Specifically, we first adapt the Melnikov method to apply to a Ricci flow perturbation and then we construct a surface which is closely related to a surface of revolution, but does not quite have rotational symmetry. This is done by adapting the Liouville metric representation of a surface of revolution. The final steps of the Melnikov method require numerical integration.

scholarly journals LOCALLY ROTATIONALLY SYMMETRIC BIANCHI TYPE-I COSMOLOGICAL MODEL IN f(T) GRAVITY: FROM EARLY TO DARK ENERGY DOMINATED UNIVERSE

2014 ◽  
Vol 23 (01) ◽  
pp. 1450004 ◽  
Author(s):  
M. E. RODRIGUES ◽  
I. G. SALAKO ◽  
M. J. S. HOUNDJO ◽  
J. TOSSA
Keyword(s):  
Dark Energy ◽  
Cosmological Model ◽  
Dark Energy Model ◽  
Bianchi Type ◽  
Rotational Symmetry ◽  
Type I ◽  
Bianchi Type I ◽  
Reconstruction Scheme ◽  
Rotationally Symmetric ◽  
The Universe

We study the locally rotational symmetry Bianchi type-I dark energy model in the framework of f(T) theory of gravity, where T denotes the torsion scalar. A viable cosmological model is undertaken and the isotropization of this latter is checked, yielding a result that reflects the real evolution of our universe. Moreover, still in the anisotropic optic, a more complicated f(T) model is obtained from the cosmological reconstruction scheme and the analysis shows that the universe is more anisotropic at the beginning if the terms of higher order in T are not considered. This means that the nonlinear model should be favored by observational data.

scholarly journals The Size of the Singular Set of a Type I Ricci Flow

2017 ◽  
Vol 27 (4) ◽  
pp. 3099-3119 ◽  
Author(s):  
Panagiotis Gianniotis
Keyword(s):  
Ricci Flow ◽  
Type I ◽  
Singular Set

scholarly journals Ancient solutions of the homogeneous Ricci flow on flag manifolds

2021 ◽  
Vol 36 (1) ◽  
pp. 99-145
Author(s):  
S. Anastassiou ◽  
I. Chrysikos
Keyword(s):  
Fixed Points ◽  
Ricci Flow ◽  
Flag Manifold ◽  
Einstein Metric ◽  
Flag Manifolds ◽  
Type I ◽  
Poincaré Compactification ◽  
The Past ◽  
Ancient Solutions ◽  
Pass Through

For any flag manifold M=G/K of a compact simple Lie group G we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. Such solutions pass through an invariant Einstein metric on M, and by [13] they must develop a Type I singularity in their extinction finite time, and also to the past. To illustrate the situation we engage ourselves with the global study of the dynamical system induced by the unnormalized Ricci flow on any flag manifold M=G/K with second Betti number b2(M) = 1, for a generic initial invariant metric. We describe the corresponding dynamical systems and present non-collapsed ancient solutions, whose α-limit set consists of fixed points at infinity of MG. Based on the Poincaré compactification method, we show that these fixed points correspond to invariant Einstein metrics and we study their stability properties, illuminating thus the structure of the system’s phase space.

scholarly journals On Type-I singularities in Ricci flow

2011 ◽  
Vol 19 (5) ◽  
pp. 905-922 ◽  
Author(s):  
Joerg Enders ◽  
Reto Müller ◽  
Peter M. Topping
Keyword(s):  
Ricci Flow ◽  
Type I
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