## Tohoku Mathematical Journal

### Quasi-Einstein totally real submanifolds of the nearly Kähler $6$-sphere

#### Article information

Source
Tohoku Math. J. (2) Volume 51, Number 4 (1999), 461-478.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178224715

Digital Object Identifier
doi:10.2748/tmj/1178224715

Mathematical Reviews number (MathSciNet)
MR1725622

Zentralblatt MATH identifier
0990.53014

#### Citation

Deszcz, Ryszard; Dillen, Franki; Verstraelen, Leopold; Vrancken, Luc. Quasi-Einstein totally real submanifolds of the nearly Kähler $6$-sphere. Tohoku Math. J. (2) 51 (1999), no. 4, 461--478. doi:10.2748/tmj/1178224715. https://projecteuclid.org/euclid.tmj/1178224715.

#### References

• [B] D. E BLAIR, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. vol. 509, Springer, Berlin, 1976.
• [BVW] J. BOLTON, L. VRANCKEN AND L M WOODWARD, On almost complex curves in the nearly Kahle 6-sphere, Quart. J Math. Oxford Ser (2) 45 (1994), 407-427.
• [Cal] E. CALABI, Minimal immersions of surfaces into Euclidean spheres, J Differential Geom 1 (1967), 111-125
• [Ca2] E. CALABI, Construction and properties of some 6-dimensional almost complex manifolds, Tran Amer. Math. Soc 87 (1958), 407-438
• [C] B -Y CHEN, Some pinching and classification theorems for minimal submanifolds, Arch Math. 6 (1993), 568-578.
• [CDVV1] B -Y CHEN, F DILLEN, L VERSTRAELEN AND L. VRANCKEN, Two equivariant totally real immer sions into the nearly Kahler 6-sphere and their characterization, Japan. J. Math. 21 (1995), 207-222.
• [CDVV2] B -Y CHEN, F DILLEN, L VERSTRAELEN AND L VRANCKEN, Characterizing a class of totally rea submanifolds of S6(l) by their sectional curvatures, Thoku Math. J 47 (1995), 185-198
• [DV] F DILLEN AND L VRANCKEN, Totally real submanifolds in S6 satisfying Chen's equality, Tran Amer Math Soc.348 (1996), 1633-1646
• [DVV] F DILLEN, L. VERSTRAELEN AND L VRANCKEN, Classification of totally real 3-dimensional sub manifolds of S6(l) with K 1/16, J. Math. Soc Japan 42 (1990), 565-584
• [El] N EJIRI, Totally real submanifolds in a 6-sphere, Proc Amer Math Soc 83 (1981), 759-76
• [E2] N EJIRI, Equivariant minimal immersions of S2 into S2m, Trans Amer Math. Soc 297 (1986), 105 124
• [HL] R HARVEY AND H B. LAWSON, Calibrated geometries, Acta Math. 148 (1982), 47-15
• [M] K MASHIMO, Homogeneous totally real submanifolds of S6(l), Tsukuba J. Math 9 (1985), 185-20
• [S] K SEKIGAWA, Almost complex submanifolds of a 6-dimensional sphere, Kodai Math J 6 (1983), 174-185
• [Sp] M SPIVAK, A Comprehensive Introduction to Differential Geometry, Vol. 1, Publish or Perish, Hous ton, 1970
• [Ver] L VERSTRAELEN, Comments on Pseudo-Symmetry in the Sense of Ryszard Deszcz, Geometry an Topology of Submanifolds VI, World Scientific, Singapore, 1994, pp 199-209.
• [V] L VRANCKEN, Locally symmetric submanifolds of the nearly Kahler S6, Algebras Groups Geom. (1988), 369-394.
• [W] R M W. WOOD, Framing the exceptional Lie group G^, Topology 15 (1976), 303-32