The Ricci Flow Equation and Poincaré Conjecture

2015 ◽  
pp. 21-29
Author(s):  
Amiya Mukherjee
Keyword(s):  
Ricci Flow ◽  
Flow Equation ◽  
Poincare Conjecture

scholarly journals Deformed $$\sigma $$-models, Ricci flow and Toda field theories

2021 ◽  
Vol 111 (6) ◽  
Author(s):  
Dmitri Bykov ◽  
Dieter Lüst
Keyword(s):  
Sigma Models ◽  
Ricci Flow ◽  
Flag Manifold ◽  
Flow Equation ◽  
Target Space ◽  
Field Theories ◽  
Two Dimensional

AbstractIt is shown that the Pohlmeyer map of a $$\sigma $$ σ -model with a toric two-dimensional target space naturally leads to the ‘sausage’ metric. We then elaborate the trigonometric deformation of the $$\mathbb {CP}^{n-1}$$ CP n - 1 -model, proving that its T-dual metric is Kähler and solves the Ricci flow equation. Finally, we discuss a relation between flag manifold $$\sigma $$ σ -models and Toda field theories.

Arbeitsgemeinschaft: Ricci Flow and the Poincaré Conjecture

2008 ◽  
pp. 2621-2654
Author(s):  
Klaus Ecker ◽  
Burkhard Wilking
Keyword(s):  
Ricci Flow ◽  
Poincare Conjecture

RICCI FLOW EQUATION ON C-REDUCIBLE METRICS

2011 ◽  
Vol 08 (04) ◽  
pp. 773-781 ◽  
Author(s):  
NASRIN SADEGHZADEH ◽  
ASSADOLLAH RAZAVI
Keyword(s):  
Fixed Point ◽  
Ricci Flow ◽  
Einstein Metrics ◽  
Flow Equation ◽  
Finsler Metrics

This paper focuses on the study of a deformation of Finsler metrics satisfying Ricci flow equation. We will prove that every deformation of Randers (Kropina)-metrics satisfying Ricci flow equation is Einstein, we will also show that a deformation of Einstein metrics with initial Randers (Kropina)-metrics remains Randers (Kropina). In other words the deformation of Randers (or Kropina)-metrics is exactly the fixed point of (un-normal and normal) Ricci flow equation.

scholarly journals Non-singular solutions to the normalized Ricci flow equation

2007 ◽  
Vol 340 (3) ◽  
pp. 647-674 ◽  
Author(s):  
Fuquan Fang ◽  
Yuguang Zhang ◽  
Zhenlei Zhang
Keyword(s):  
Ricci Flow ◽  
Flow Equation ◽  
Singular Solutions ◽  
Normalized Ricci Flow

A MECHANICS FOR THE RICCI FLOW

2009 ◽  
Vol 06 (05) ◽  
pp. 759-767 ◽  
Author(s):  
S. ABRAHAM ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
JOSÉ M. ISIDRO ◽  
J. L. G. SANTANDER
Keyword(s):  
Ricci Flow ◽  
Jacobi Equation ◽  
Classical Mechanics ◽  
Riemannian Metric ◽  
Flow Equation ◽  
Time Dependent ◽  
Dimensional Manifold ◽  
Conformally Flat ◽  
Hamilton Jacobi Equation

We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton–Jacobi equation of the mechanics so defined.

Fundamentals of the Ricci flow equation

2006 ◽  
pp. 95-125
Author(s):  
Bennett Chow ◽  
Peng Lu ◽  
Lei Ni
Keyword(s):  
Ricci Flow ◽  
Flow Equation

scholarly journals Sasaki–Ricci flow equation on five-dimensional Sasaki–Einstein space Yp,q

2020 ◽  
Vol 35 (14) ◽  
pp. 2050114
Author(s):  
Mihai Visinescu
Keyword(s):  
Ricci Flow ◽  
Contact Structure ◽  
Flow Equation ◽  
Einstein Space ◽  
Explicit Solutions

We analyze the transverse Kähler–Ricci flow equation on Sasaki-Einstein space [Formula: see text]. Explicit solutions are produced representing new five-dimensional Sasaki structures. Solutions which do not modify the transverse metric preserve the Sasaki–Einstein feature of the contact structure. If the transverse metric is altered, the deformed metrics remain Sasaki, but not Einstein.

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