Abstract
AbstractWe compute the Morse index of a critical submanifold of the energy functional on the loop space of a manifold with constant sectional curvature. The case of constant non-positive sectional curvature is a known result and the case of a sphere has been proved by Klingenberg. We adapt Klingenberg’s proof of the case of a sphere to the case of constant sectional curvature, to obtain the possible Morse indices of critical submanifolds of the energy functional.
Funder
Middle East Technical University
Publisher
Springer Science and Business Media LLC
Reference16 articles.
1. Duistermaat, J.J.: On the Morse index in variational calculus. Adv. Math. 21, 173–195 (1976)
2. Gadea, P.M., Muñoz, Masque J., Mykytuk, I.V.: Analysis and Algebra on Differentiable Manifolds: A Workbook for students and teachers, 2nd edn. Springer, London (2012)
3. Hingston, N.: Equivariant Morse theory and closed geodesics. J. Differ. Geom. 19, 85–116 (1984)
4. Kerman, E.: Action selectors and Maslov class rigidity. Internat. Math. Res. Not. 2009(23), 4395–4427 (2009)
5. Kerman, E., Şirikçi, N.I.: Maslov class rigidity for Lagrangian submanifolds via Hofer’s geometry. Comment. Math. Helv. 85, 907–949 (2010)