TOTALLY REAL SURFACES IN $S^6$

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Published: Jun 15, 2021
DOI: https://doi.org/10.5556/j.tkjm.23.1992.4522
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SHARIEF DESHMUKH
Department of Mathematics, College of Science, King, Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.

Abstract




The normal bundle $\bar \nu$ of a totally real surface $M$ in $S^6$ splits as $\bar\nu= JTM\oplus \bar\mu$ where $TM$ is the tangent bundle of $M$ and  $\bar\mu$ is sub­bundle of $\bar\nu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) \in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic).




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How to Cite
DESHMUKH, S. (2021). TOTALLY REAL SURFACES IN $S^6$ . Tamkang Journal of Mathematics, 23(1), 11–14. https://doi.org/10.5556/j.tkjm.23.1992.4522
Issue
Vol. 23 No. 1 (1992)
Section
Papers
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References

N. Ejiri, "Totally real submanifolds in a 6-sphere", Proc. Amer. Math. Soc. 83, pp. 759- 763, 1981.

A. Gray, "Almost complex submanifolds_of the six sphere", Proc. Amer. Math. Soc. 20, pp. 277-279, 1969.

S. Kobayashi and I<. Nomizu, Foundations of Differential Geometry, Vol. II, John Wiley and Sons, N. Y. (1964).