scholarly journals A new curvature condition preserved by the Ricci flow

2012 ◽  
Vol 387 (2) ◽  
pp. 791-798
Author(s):  
Xiang Gao
Keyword(s):  
Ricci Flow ◽  
Curvature Condition

scholarly journals A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities

2013 ◽  
Vol 2013 (679) ◽  
pp. 223-247 ◽  
Author(s):  
Burkhard Wilking
Keyword(s):  
Lie Algebra ◽  
Ricci Flow ◽  
Algebraic Approach ◽  
Kähler Manifold ◽  
Curvature Condition ◽  
Bisectional Curvature ◽  
Harnack Inequalities ◽  
Kahler Manifold ◽  
Positive Bisectional Curvature ◽  
Compact Kähler Manifold

Abstract We consider a subset S of the complex Lie algebra 𝔰𝔬(n, ℂ) and the cone C(S) of curvature operators which are nonnegative on S. We show that C(S) defines a Ricci flow invariant curvature condition if S is invariant under AdSO(n, ℂ). The analogue for Kähler curvature operators holds as well. Although the proof is very simple and short, it recovers all previously known invariant nonnegativity conditions. As an application we reprove that a compact Kähler manifold with positive orthogonal bisectional curvature evolves to a manifold with positive bisectional curvature and is thus biholomorphic to ℂℙn. Moreover, the methods can also be applied to prove Harnack inequalities.

Ricci Flow on Quasi Einstein Manifold

2010 ◽  
Vol 0 (-1) ◽  
pp. 447-454
Author(s):  
A. Bhattacharyya ◽  
T. De
Keyword(s):  
Ricci Flow ◽  
Einstein Manifold

scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

scholarly journals Sliding Mode Control and Geometrization Conjecture in Seismic Response

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 353
Author(s):  
Ligia Munteanu ◽  
Dan Dumitriu ◽  
Cornel Brisan ◽  
Mircea Bara ◽  
Veturia Chiroiu ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Ricci Flow ◽  
Lyapunov Functions ◽  
Seismic Waves ◽  
Sliding Mode ◽  
Flow Process ◽  
Mode Control ◽  
Finite Period ◽  
The Stability ◽  
Story Building

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

scholarly journals Ancient solutions for Andrews’ hypersurface flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Peng Lu ◽  
Jiuru Zhou
Keyword(s):  
Ricci Flow ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Euclidean Spaces ◽  
Round Cylinder ◽  
Ancient Solutions ◽  
Singular Time

AbstractWe construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. Andrews in 1994.As time {t\rightarrow 0^{-}} the solutions collapse to a round point where 0 is the singular time. But as {t\rightarrow-\infty} the solutions become more and more oval. Near the center the appropriately-rescaled pointed Cheeger–Gromov limits are round cylinder solutions {S^{J}\times\mathbb{R}^{n-J}}, {1\leq J\leq n-1}. These results are the analog of the corresponding results in Ricci flow ({J=n-1}) and mean curvature flow.

scholarly journals Ricci flow on surfaces with cusps

2009 ◽  
Vol 345 (4) ◽  
pp. 819-834 ◽  
Author(s):  
Lizhen Ji ◽  
Rafe Mazzeo ◽  
Natasa Sesum
Keyword(s):  
Ricci Flow
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