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The Shape Operator of Real Hypersurfaces in S 6 (1)

Author

Listed:
  • Djordje Kocić

    (Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Miroslava Antić

    (Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

Abstract

The aim of the paper is to present two results concerning real hypersurfaces in the six-dimensional sphere S 6 ( 1 ) . More precisely, we prove that real hypersurfaces with the Lie-parallel shape operator A must be totally geodesic hyperspheres. Additionally, we classify real hypersurfaces in a nearly Kähler sphere S 6 ( 1 ) whose Lie derivative of the shape operator coincides with its covariant derivative.

Suggested Citation

  • Djordje Kocić & Miroslava Antić, 2024. "The Shape Operator of Real Hypersurfaces in S 6 (1)," Mathematics, MDPI, vol. 12(11), pages 1-8, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1668-:d:1402792
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