Equivariant minimal immersions of $S^ 2$ into $S^ {2m}(1)$
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- by Norio Ejiri
- Trans. Amer. Math. Soc. 297 (1986), 105-124
- DOI: https://doi.org/10.1090/S0002-9947-1986-0849470-2
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Abstract:
We classify the directrix curves associated with equivariant minimal immersions of ${S^2}$ into ${S^{2m}}(1)$ and obtain some applications.References
- O. Borůvka, Sur les surfaces représentées par les fonctions sphériques de prémiere espèce, J. Math. Pures Appl. 12 (1933), 337-383.
- João Lucas Marquês Barbosa, On minimal immersions of $S^{2}$ into $S^{2m}$, Trans. Amer. Math. Soc. 210 (1975), 75–106. MR 375166, DOI 10.1090/S0002-9947-1975-0375166-2
- João Lucas Marquês Barbosa, An extrinsic rigidity theorem for minimal immersions from $S^{2}$ into $S^{n}$, J. Differential Geometry 14 (1979), no. 3, 355–368 (1980). MR 594706
- Robert L. Bryant, Submanifolds and special structures on the octonians, J. Differential Geometry 17 (1982), no. 2, 185–232. MR 664494
- Robert L. Bryant, Conformal and minimal immersions of compact surfaces into the $4$-sphere, J. Differential Geometry 17 (1982), no. 3, 455–473. MR 679067
- Eugenio Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Differential Geometry 1 (1967), 111–125. MR 233294
- Shiing Shen Chern, On the minimal immersions of the two-sphere in a space of constant curvature, Problems in analysis (Sympos. in honor of Salomon Bochner, Princeton Univ., Princeton, N.J., 1969) Princeton Univ. Press, Princeton, N.J., 1970, pp. 27–40. MR 0362151
- Norio Ejiri, Totally real submanifolds in a $6$-sphere, Proc. Amer. Math. Soc. 83 (1981), no. 4, 759–763. MR 630028, DOI 10.1090/S0002-9939-1981-0630028-6
- Norio Ejiri, The index of minimal immersions of $S^{2}$ into $S^{2n}$, Math. Z. 184 (1983), no. 1, 127–132. MR 711733, DOI 10.1007/BF01162011
- Joseph Erbacher, Reduction of the codimension of an isometric immersion, J. Differential Geometry 5 (1971), 333–340. MR 288701
- Reese Harvey and H. Blaine Lawson Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157. MR 666108, DOI 10.1007/BF02392726
- Peter Li and Shing Tung Yau, A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent. Math. 69 (1982), no. 2, 269–291. MR 674407, DOI 10.1007/BF01399507 K. Mashimo, Minimal immersions of $3$-dimensional sphere into sphere (preprint).
- Kouei Sekigawa, Almost complex submanifolds of a $6$-dimensional sphere, Kodai Math. J. 6 (1983), no. 2, 174–185. MR 702939
- James Simons, Minimal varieties in riemannian manifolds, Ann. of Math. (2) 88 (1968), 62–105. MR 233295, DOI 10.2307/1970556
- Karen K. Uhlenbeck, Equivariant harmonic maps into spheres, Harmonic maps (New Orleans, La., 1980) Lecture Notes in Math., vol. 949, Springer, Berlin-New York, 1982, pp. 146–158. MR 673590
- Luc Gheysens, Paul Verheyen, and Leopold Verstraelen, Characterization and examples of Chen submanifolds, J. Geom. 20 (1983), no. 1, 47–62. MR 710064, DOI 10.1007/BF01917994
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 297 (1986), 105-124
- MSC: Primary 58E12; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9947-1986-0849470-2
- MathSciNet review: 849470