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

Djordje Kocić () and Miroslava Antić
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Djordje Kocić: Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia
Miroslava Antić: Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia

Mathematics, 2024, vol. 12, issue 11, 1-8

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.

Keywords: Hopf hypersurfaces; nearly Kähler manifolds; real hypersurfaces; shape operator; Lie derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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