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On the stability of the L-p-norm of the Riemannian curvature tensor

Maity, Soma (2014) On the stability of the L-p-norm of the Riemannian curvature tensor. In: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 124 (3). pp. 383-409.

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Official URL: http://dx.doi.org/ 10.1007/s12044-014-0187-2

Abstract

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the INDIAN ACAD SCIENCES
Keywords: Riemannian functional; critical point; stability; local minima
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 08 Nov 2014 05:15
Last Modified: 08 Nov 2014 05:15
URI: http://eprints.iisc.ac.in/id/eprint/50176

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