On the geometry of ζ-Ricci solitons in the nearly Kaehler 6-Sphere

Pooja Bansal () and Rakesh Kumar ()
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Pooja Bansal: University of Delhi
Rakesh Kumar: Punjabi University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 484-491

Abstract: Abstract In the present paper, we derive conditions for real hypersurface of a nearly Kaehler $${\mathbb {S}}^{6}$$ S 6 endowed with quarter-symmetric metric connection to be a Hopf hypersurface. By finding its geometric application using Hopf foliation, we demonstrate that if a real hypersurface of nearly Kaehler $${\mathbb {S}}^{6}$$ S 6 endowed with quarter-symmetric metric connection is an $$\zeta $$ ζ -Ricci soliton then it is an $$\zeta $$ ζ -Einstein real hypersurface and in further geometric analysis, we prove that it is congruent to an open segment of a totally-geodesic hypersphere or equivalently, a tube over an almost complex curve in $${\mathbb {S}}^{6}$$ S 6 .

Keywords: Real hypersurfaces; Hopf foliation; Nearly Kaehler $${\mathbb {S}}^{6}$$ S 6; Quarter-symmetric metric connection; $$\zeta $$ ζ -Ricci soliton; 53C20; 53C45; 53C15; 53B25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00110-y

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