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On totally real surfaces of the nearly Kaehler 6-sphere

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Abstract

Let M be a minimal totally real surface of the nearly Kaehler 6-sphere. We prove that if M is homeomorphic to a sphere, then M is totally geodesic. Consequently, if M is compact and has non-negative Gaussian curvature K, then eithe K=0 or K=1. Finally, we derive from these results that if M has constant Gaussian curvature K, then either K=0 or K=1.

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Authors and Affiliations

  1. Department of Mathematics, Katholieke Universiteit Leuven, B-3030, Leuven, Belgium

    F. Dillen, L. Verstraelen & L. Vrancken

  2. Department of Mathematics, University of Craców, 30-059, Craców, Poland

    B. Opozda

Authors
  1. F. Dillen
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  2. B. Opozda
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  3. L. Verstraelen
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  4. L. Vrancken
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Additional information

Aspirant Navorser N.F.W.O. (Belgium).

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Dillen, F., Opozda, B., Verstraelen, L. et al. On totally real surfaces of the nearly Kaehler 6-sphere. Geom Dedicata 27, 325–334 (1988). https://doi.org/10.1007/BF00181497

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  • DOI: https://doi.org/10.1007/BF00181497

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