The normal curvature of totally real submanifolds of S6(1)
Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 199-204

Voir la notice de l'article provenant de la source Cambridge University Press

We prove the pointwise inequality 0 ≥ ρ + ρ⊥ – 1 involving the normalized scalar curvature ρ and normal scalar curvature ρ⊥ of a totally real 3-dimensional submanifold of the nearly Kaehler 6-sphere. Further we classify submanifolds realizing the equality in this inequality.
Smet, P. J. De; Dillen, F.; Verstraelen, L.; Vrancken, L. The normal curvature of totally real submanifolds of S6(1). Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 199-204. doi: 10.1017/S0017089500032511
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[1] 1.Bolton, J., Vrancken, L. and Woodward, L. M., On almost complex curves in the nearly Kähler 6-sphere, Quart. J. Math. Oxford Ser. (2) 45 (1994), 407–,427. Google Scholar | DOI

[2] 2.Calabi, E., Construction and properties of some 6-dimensional almost complex manifolds, Trans. Amer. Math. Soc. 87 (1958), 407–438. Google Scholar | DOI

[3] 3.Chen, B. Y., Some pinching and classification theorems for minimal submanifolds, Arch Math. (Basel) 60 (1993), 568–578. Google Scholar

[4] 4.Chen, B. Y., Mean curvature and shape operator of isometric immersions in real-space-forms, Glasgow Math. J. 38 (1996), 87–97. Google Scholar | DOI

[5] 5.Chen, B.-Y., Dillen, F., Verstraelen, L. and Vrancken, L., Two equivariant totally real immersions into the nearly Kähler 6-sphere and their characterization, Japanese J. Math. (N.S.) 21 (1995), 207–222. Google Scholar | DOI

[6] 6.Chen, B. Y., Dillen, F., Verstraelen, L. and Vrancken, L., Characterizing a class of totally real submanifolds of S6(l) by their sectional curvatures, Tōhoku Math. J. 47 (1995), 185–198. Google Scholar

[7] 7.De Smet, P. J., Dillen, F., Verstraelen, L. and Vrancken, L., A pointwise inequality in submanifold theory (1996), Arch. Math. (Brno), to appear. Google Scholar

[8] 8.Dillen, F., Verstraelen, L. and Vrancken, L., Classification of totally real 3-dimensional submanifolds of S6(1) with K ≥ 1/16; J. Math. Soc. Japan 42 (1990), 565–584. Google Scholar | DOI

[9] 9.Dillen, F. and Vrancken, L., Totally real Submanifolds in S 6 satisfying Chen's Equality, Trans. Amer. Math. Soc. 348 (1996), 1633–1646. Google Scholar

[10] 10.Ejiri, N., Totally real submanifolds in a 6-sphere, Proc. Amer. Math. Soc. 83 (1981), 759–763. Google Scholar | DOI

[11] 11.Guadalupe, I. V. and Rodriguez, L., Normal curvature of surfaces in space forms, Pacific J. Math. 106 (1983), 95–103. Google Scholar | DOI

[12] 12.Vrancken, L., Locally symmetric submanifolds of the nearly Kaehler S 6, Algebras, Groups and Geometries 5 (1988), 369–394. Google Scholar

[13] 13.Wintgen, P., Sur l'inégalité de Chen-Willmore, C. R. Acad. Sc. Paris 288 (1979), 993–995. Google Scholar

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