Hoph Hypersurfaces of Sasakian Space Form with Parallel Ricci Operator Esmaiel Abedi, Mohammad Ilmakchi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Subject Areas : Statistics

Esmaiel Abedi ^{1 *} , Mohammad Ilmakchi ²

1 - Azarbaijan Shahid Madani University
2 - Azarbaijan shahid madani university

Received: 2017-06-22 Accepted : 2020-02-27 Published : 2020-07-01

Keywords: ابررویه, زیرخمینه حاصلضربی, عملگر شکل, خمیدگی اصلی, عملگر ریچی, فضا فرم ساساکی,

Abstract :

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, the shape operator A of M^2n had been constant fixed main curvatures and the maximum of the main curvatures has three distinct. In the second case, the shape operator A of M^2n on D united with zero and M^2n has sn integral manifold that takes the structure of Sasakian space form. Then first by defining a vector field in M^2n show that the integral curve of this vector field in M^2n is geodesy and also by defining a hypersurface in M^2n show that this hypersurface in M^2n is totally geodesic and finally; we show that M^2n is locally the product of these totally geodesic hypersurface with the geodesy curve.

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