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On the Stability of Certain Riemannian Functionals

Electronic Theses of Indian Institute of Science

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Title On the Stability of Certain Riemannian Functionals
 
Creator Maity, Soma
 
Subject Riemannian Geometry
Ricci Curvature
Curvature (Mathematics)
Riemannian Manifolds
Riemannian Functionals
Riemannain Metrics
Riemannian Metric
Space Forms
Geometry
 
Description Given a compact smooth manifold Mn without boundary and n ≥ 3, the Lp-norm of the curvature tensor,
defines a Riemannian functional on the space of Riemannian metrics with unit volume M1. Consider C2,α-topology on M1 Rp remains invariant under the action of the group of diffeomorphisms D of M. So, Rp is defined on M1/ D. Our first result is that Rp restricted to the space M1/D has strict local minima at Riemannian metrics with constant sectional curvature for certain values of p. The product of spherical space forms and the product of compact hyperbolic manifolds are also critical point for Rp if they are product of same dimensional manifolds. We prove that these spaces are strict local minima for Rp restricted to M1/D. Compact locally symmetric isotropy irreducible metrics are critical points for Rp. We give a criteria for the local minima of Rp restricted to the conformal class of metrics of a given irreducible symmetric metric. We also prove that the metrics with constant bisectional curvature are strict local minima for Rp restricted to the space of Kahlar metrics with unite volume quotient by D.
Next we consider the Riemannian functional given by

In [GV], M. J. Gursky and J. A. Viaclovsky studied the local properties of the moduli space of critical metrics for the functional Ric2.We generalize their results for any p > 0.
 
Contributor Seshadri, Harish
 
Date 2018-03-05T18:55:23Z
2018-03-05T18:55:23Z
2018-03-06
2012
 
Type Thesis
 
Identifier http://hdl.handle.net/2005/3230
http://etd.ncsi.iisc.ernet.in/abstracts/4089/G25418-Abs.pdf
 
Language en_US
 
Relation G25418