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On an ODE Associated to the Ricci Flow

Electronic Theses of Indian Institute of Science

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Title On an ODE Associated to the Ricci Flow
 
Creator Bhattacharya, Atreyee
 
Subject Riemannian Manifolds
Curvature
Ricci Flow
Ricci-Flat 4-Manifolds
Algebraic Curvature Operators
Vector Fields
Ricci-Flat Kahler Surfaces
Riemannian Curvature Operator
Kahler Manifolds
Ordinary Differential Equations
Differential Geometry
Integral Curves
Geometry
 
Description We discuss two topics in this talk. First we study compact Ricci-flat four dimensional manifolds without boundary and obtain point wise restrictions on curvature( not involving global quantities such as volume and diameter) which force the metric to be flat. We obtain the same conclusion for compact Ricci-flat K¨ahler surfaces with similar but weaker restrictions on holomorphic sectional curvature.
Next we study the reaction ODE associated to the evolution of the Riemann curvature operator along the Ricci flow. We analyze the behavior of this ODE near algebraic curvature operators of certain special type that includes the Riemann curvature operators of various(locally) symmetric spaces. We explicitly show the existence of some solution curves to the ODE connecting the curvature operators of certain symmetric spaces. Although the results of these two themes are different, the underlying common feature is the reaction ODE which plays an important role in both.
 
Contributor Seshadri, Harish
 
Date 2018-04-18T10:17:54Z
2018-04-18T10:17:54Z
2018-04-18
2013
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3427
http://etd.iisc.ernet.in/abstracts/4294/G25939-Abs.pdf
 
Language en_US
 
Relation G25939