Abstract
The first two sections of this chapter are an introduction to Riemannian geometry. It is not self-contained, and precise references are provided when necessary. However, we chosed to give some proofs which have a metric flavour.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
V. I. Arnold, Singularities of systems of rays, Russian Math. Surveys 38 (1983), 87–176.
E. Beckenbach, T. Rado, Subharmonic functions and surfaces of negative curvature, Trans. Amer. Math. Soc. 35 (1933), 662–674.
D. Bennequin, Problèmes elliptiques, surfaces de Riemann et structures sym-plectiques, in Séminaire Bourhaki, Astérisque 145–146 (1987), 111–136.
F. Bernstein, Über die isoperimetrische Eigenschaft des Kreises auf der Kugeloberfläsche und in der Ebene, Math. Ann. 60 (1905), 117–136.
A. Besse, Manifolds, all of whose geodesics are closed, Springer, 1975.
G. Bol, Isoperimetrisch Ungleichungen für Bereiche auf Flächen, Jahresbericht d. Deutschen Mathem. Vereinigung 3 (1951), 219–257.
Y. Burago, V. Zallgaller, Geometric Inequalities, Springer, 1988 (for the English translation).
J. Cheeger, D. Ebin, Comparison theorems in Riemannian Geometry, North-Holland, 1975.
M. DoCarmo, Riemannian Geometry, Birkhaüser, 1990.
H.M. Farkas, I. Kra, Riemann Surfaces, Springer, 1992 (second edition).
J. Duval, Compacité des J-courbes, le cas simple des J-droites d’un pseudoplan, preprint (1987).
F. Fiala, Le problème des isopérimétres sur les surfaces ouvertes à courbure positive, Comment. Math. Helv. 13 (1940–41), 293–345.
S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer, 1990 (second edition).
M. Gromov, J. Lafontaine, P. Pansu, Structures métriques pour les variétés riemanniennes, Cedic-Nathan, diffusé par la Société Mathématique de France, 1981.
W. Klingenberg, Riemannian Geometry, deGruyter, 1982.
B. Lawson, Minimal manifolds in real and complex Geometry, Séminaire de Mathématiques Supérieures de Montréal, 1973.
J. Milnor, Morse theory, Princeton University Press, 1963.
R. Ossermann, The isoperimetric inequality, Bull. of Amer. Math. Soc. 84 (1979), 1182–1238.
Séminaire Orsay, Travaux de Thurston sur les surfaces, Astérisque 66–67 (1979).
Séminaire Palaiseau, Théorie des variétés minimales et applications, Astérisque 154–155 (1987).
S. Peters, Cheeger’s fineteness theorem for diffeomorphism classes of Riemannian manifolds, J. für die reine und angewandte Math. 349 (1988), 77–82.
E. Schmidt, Über die isoperimetrische Aufgabe im n-dimensionalen Raum konstanter negativer Krümmung, Math. Z. 46 (1940), 204–230.
J. Wolfson, Gromov’s compactness of pseudo-holomorphic curves and Symplectic Geometry, J. of Diff. Geom. (1988), 383–405.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Basel AG
About this chapter
Cite this chapter
Lafontaine, J. (1994). Some relevant Riemannian geometry. In: Audin, M., Lafontaine, J. (eds) Holomorphic Curves in Symplectic Geometry. Progress in Mathematics, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8508-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8508-9_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9656-6
Online ISBN: 978-3-0348-8508-9
eBook Packages: Springer Book Archive