H°-type Riemannian metrics on the space of planar curves

Quarterly of Applied Mathematics

Volumn 66, Issue 1, 2008, Pages 123-137

  Shah, Jayant ^a  

^a NORTHEASTERN UNIVERSITY   (United States)

Author keywords

Differential geometry; Moduli of planar curves

Indexed keywords

CONFORMAL MAPPING;

CONFORMAL FACTORS; DIFFERENTIAL GEOMETRY; GEODESIC EQUATIONS; PLANAR CURVES; RIEMANNIAN METRICS; SECTIONAL CURVATURES; SUPERLINEAR;

GEOMETRY;

EID: 46849084542     PISSN: 0033569X     EISSN: 15524485     Source Type: Journal    
DOI: 10.1090/s0033-569x-07-01084-4     Document Type: Article

References (8)

1. A. L. Besse, "Einstein manifolds", Springer-Verlag, 1987. MR867684 (88f:53087)
2. P. Michor and D. Mumford, "Riemannian geometries on spaces of plane curves", arXiv:math.DG/0312384, v2, Sep. 22, 2004. MR2201275 (2007a:58007)
3. P. Michor and D. Mumford, "An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach", Tech. Report, ESI Preprint #1798, 2005.
4. E. Klassen, A. Srivastava, W. Mio, and S. H. Joshi, "Analysis of planar shapes using geodesic paths on shape spaces", IEEE Trans. PAMI, 26(3), pp. 372-383, 2003.
5. W. Mio and A. Srivastava, "Elastic-string models for representation and analysis of planar shapes", CVPR(2), 2004, pp. 10-15.
6. W. Mio, A. Srivastava, and S. H. Joshi, "On shape of plane elastic curves", International Journal of Computer Vision, 73(3), pp. 307-324. 7 A. Yezzi and A. Mennucci, "Conformal Riemannian metrics in space of curves", EUSIPCO04, MIA, 2004.
7. A. Yezzi and A. Mennucci, "Metrics in the space of curves", arXiv:math.DG/0412454, v2, May 25, 2005.
8. L. Younes, "Computable elastic distances between shapes," SIAM J. Appl. Math., 58 (1998), pp. 565-586. MR1617630 (99c:68221)