A rigidity result for holomorphic immersions of surfaces in $\textbf {C}\textrm {P}^ n$
HTML articles powered by AMS MathViewer
- by Marco Rigoli PDF
- Proc. Amer. Math. Soc. 93 (1985), 317-320 Request permission
Abstract:
A pinching condition for the Gaussian curvature implies rigidity.References
- Eugenio Calabi, Isometric imbedding of complex manifolds, Ann. of Math. (2) 58 (1953), 1–23. MR 57000, DOI 10.2307/1969817
- E. Calabi, Metric Riemann surfaces, Contributions to the theory of Riemann surfaces, Annals of Mathematics Studies, no. 30, Princeton University Press, Princeton, N.J., 1953, pp. 77–85. MR 0061675
- H. Blaine Lawson Jr., The Riemannian geometry of holomorphic curves, Bol. Soc. Brasil. Mat. 2 (1971), no. 1, 45–62. MR 324606, DOI 10.1007/BF02584806
- Katsumi Nomizu and Brian Smyth, Differential geometry of complex hypersurfaces. II, J. Math. Soc. Japan 20 (1968), 498–521. MR 230264, DOI 10.2969/jmsj/02030498
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 317-320
- MSC: Primary 53C42; Secondary 53C55
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770544-3
- MathSciNet review: 770544