A characterization of the generalized Veronese surfaces
HTML articles powered by AMS MathViewer
- by Takehiro Itoh PDF
- Proc. Amer. Math. Soc. 104 (1988), 571-576 Request permission
Abstract:
We prove that compact $m$-regular minimal surfaces in a sphere are generalized Veronese surfaces if the Gaussian curvature satisfies an inequality.References
- Eugenio Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Differential Geometry 1 (1967), 111–125. MR 233294
- Manfredo P. do Carmo and Nolan R. Wallach, Minimal immersions of spheres into spheres, Ann. of Math. (2) 93 (1971), 43–62. MR 278318, DOI 10.2307/1970752
- Takehiro Itoh, Minimal surfaces in a Riemannian manifold of constant curvature, K\B{o}dai Math. Sem. Rep. 25 (1973), 202–214. MR 317240
- Takehiro Itoh, On minimal surfaces in a Riemannian manifold of constant curvature, Math. J. Okayama Univ. 17 (1974), 19–38. MR 365425
- Tominosuke Ôtsuki, Minimal submanifolds with $m$-index $2$ and generalized Veronese surfaces, J. Math. Soc. Japan 24 (1972), 89–122. MR 295259, DOI 10.2969/jmsj/02410089
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 571-576
- MSC: Primary 53A10; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1988-0962830-1
- MathSciNet review: 962830