The Riemannian L2 topology on the manifold of Riemannian metrics

Annals of Global Analysis and Geometry

Volumn 39, Issue 2, 2011, Pages 131-163

  Clarke, Brian ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Manifold of Riemannian metrics; Manifold of Riemannian structures; Superspace

Indexed keywords

EID: 78650961987     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10455-010-9227-z     Document Type: Article

References (13)

1. Bogachev V. I.: Measure Theory, vols. I & II. Springer, Berlin (2007).
2. Bourguignon J.-P.: Une stratification de l'espace des structures riemanniennes. Compos. Math. 30(1), 1-41 (1975).
3. 2 metric. Ph. D. Thesis, University of Leipzig, 2009, http://arxiv. org/abs/0904. 0159v1.
4. Clarke, B.: The completion of the manifold of Riemannian metrics, preprint, http://arxiv. org/abs/0904. 0177v1.
5. Clarke, B.: The metric geometry of the manifold of Riemannian metrics. Calc. Var. Partial Differential Equations, pp. 1-13. Springer, Berlin/Heidelberg (2010).
6. Ebin, D. G.: The manifold of Riemannian metrics. In: Chern, S.-S., Smale, S. (eds.) Global Analysis. Proceedings of Symposia in Pure Mathematics, vol. 15, pp. 11-40. American Mathematical Society, Providence, RI (1970).
7. Freed D. S., Groisser D.: The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group. Michigan Math. J. 36, 323-344 (1989).
8. Gil-Medrano, O., Michor, P. W.: The Riemannian manifold of all Riemannian metrics. Q. J. Math. Oxford Ser. (2) 42(166), 183-202 (1991), http://arxiv. org/abs/arXiv: math/9201259.
9. Gromov M.: Metric Structures for Riemannian and Non-Riemannian Spaces. Birkhäuser, Boston (2007).
10. Michor, P. W., Mumford, D.: Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Doc. Math. 10, 217-245 (2005), http://arxiv. org/abs/arXiv: math/0409303.
11. Michor, P. W., Mumford, D.: Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc. (JEMS) 8(1), 1-48 (2006), http://arxiv. org/abs/math. DG/0312384.
12. Rana I. K.: An Introduction to Measure and Integration, 2nd ed. Graduate Studies in Mathematics, vol. 45. American Mathematical Society, Providence, RI (2002).
13. Tromba A. J.: Teichmüller Theory in Riemannian Geometry. Birkhäuser, Basel (1992).