Equivariant minimal immersions of into
Author:
Norio Ejiri
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We classify the directrix curves associated with equivariant minimal immersions of into
and obtain some applications.
- [1] O. Borůvka, Sur les surfaces représentées par les fonctions sphériques de prémiere espèce, J. Math. Pures Appl. 12 (1933), 337-383.
- [2] João Lucas Marquês Barbosa, On minimal immersions of 𝑆² into 𝑆^{2𝑚}, Trans. Amer. Math. Soc. 210 (1975), 75–106. MR 375166, https://doi.org/10.1090/S0002-9947-1975-0375166-2
- [3] João Lucas Marquês Barbosa, An extrinsic rigidity theorem for minimal immersions from 𝑆² into 𝑆ⁿ, J. Differential Geometry 14 (1979), no. 3, 355–368 (1980). MR 594706
- [4] Robert L. Bryant, Submanifolds and special structures on the octonians, J. Differential Geometry 17 (1982), no. 2, 185–232. MR 664494
- [5] 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
- [6] Eugenio Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Differential Geometry 1 (1967), 111–125. MR 233294
- [7] Shiing Shen Chern, On the minimal immersions of the two-sphere in a space of constant curvature, Problems in analysis (Lectures at the Sympos. in honor of Salomon Bochner, Princeton Univ., Princeton, N.J., 1969) Princeton Univ. Press, Princeton, N.J., 1970, pp. 27–40. MR 0362151
- [8] Norio Ejiri, Totally real submanifolds in a 6-sphere, Proc. Amer. Math. Soc. 83 (1981), no. 4, 759–763. MR 630028, https://doi.org/10.1090/S0002-9939-1981-0630028-6
- [9] Norio Ejiri, The index of minimal immersions of 𝑆² into 𝑆²ⁿ, Math. Z. 184 (1983), no. 1, 127–132. MR 711733, https://doi.org/10.1007/BF01162011
- [10] Joseph Erbacher, Reduction of the codimension of an isometric immersion, J. Differential Geometry 5 (1971), 333–340. MR 288701
- [11] Reese Harvey and H. Blaine Lawson Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157. MR 666108, https://doi.org/10.1007/BF02392726
- [12] 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, https://doi.org/10.1007/BF01399507
- [13]
K. Mashimo, Minimal immersions of
-dimensional sphere into sphere (preprint).
- [14] Kouei Sekigawa, Almost complex submanifolds of a 6-dimensional sphere, Kodai Math. J. 6 (1983), no. 2, 174–185. MR 702939
- [15] James Simons, Minimal varieties in riemannian manifolds, Ann. of Math. (2) 88 (1968), 62–105. MR 233295, https://doi.org/10.2307/1970556
- [16] 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
- [17] Luc Gheysens, Paul Verheyen, and Leopold Verstraelen, Characterization and examples of Chen submanifolds, J. Geom. 20 (1983), no. 1, 47–62. MR 710064, https://doi.org/10.1007/BF01917994
Retrieve articles in Transactions of the American Mathematical Society with MSC: 58E12, 53C42
Retrieve articles in all journals with MSC: 58E12, 53C42
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849470-2
Article copyright:
© Copyright 1986
American Mathematical Society