Volume 7, Issue 2 (Vol.7, No. 2, 2021)                   mmr 2021, 7(2): 215-236 | Back to browse issues page

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Etemad Dehkordy A. Some Applications of Casorati Curvature for Statistical Submanifolds of Sasakian Statistical Manifolds and Locally Homogeneous, Quasi-Umbilical Hypersurfaces. mmr 2021; 7 (2) :215-236
URL: http://mmr.khu.ac.ir/article-1-2878-en.html
Isfahan University of Technology , ae110mat@cc.iut.ac.ir
Abstract:   (1190 Views)
In this paper, in the first part, the affine geometry is assumed as the main framework. Then we have a spacious explanation of necessary introduction in rather different subjects. In this part, statistical submanifolds of Sasakian statistical manifolds with constant -sectional curvature is considered as the pivotal topic. Afterwards, with a rather long process, we obtain an optimal inequalities between generalized normalized scalar curvature as an intrinsic property and 􀟜-Casorati curvature as an extrinsic property. In زthis result is existence of an inequality between normalized scalar curvature and Casorati curvature. In the second section, using Casorati curvature, with more capability than
sectional curvature, we deduce some results about locally symmetric, quasi-umbilical hypersurfaces of real space forms of zero curvature. This yields an analytical and algebraic expression for locally symmetric, quasi-umbilical hypersurfaces that concludes the usability of affine geometry in using of softwares../files/site1/files/72/4Abstract.pdf
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Type of Study: S | Subject: alg
Received: 2018/11/14 | Revised: 2021/08/7 | Accepted: 2019/10/7 | Published: 2021/09/1 | ePublished: 2021/09/1

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