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:: Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) ::
mr 2021, 7(2): 215-236 Back to browse issues page
Some Applications of Casorati Curvature for Statistical Submanifolds of Sasakian Statistical Manifolds and Locally Homogeneous, Quasi-Umbilical Hypersurfaces
Azam Etemad Dehkordy
Isfahan University of Technology , ae110mat@cc.iut.ac.ir
Abstract:   (160 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
Keywords: Statistical manifolds, Sasakian manifolds, Casorati curvature, Local homogeneous, Quasi-umbilical
Full-Text [PDF 659 kb]   (37 Downloads)    
Type of Study: S | Subject: alg
Received: 2018/11/14 | Accepted: 2019/10/7 | Published: 2021/09/1 | ePublished: 2021/09/1
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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. mr. 2021; 7 (2) :215-236
URL: http://mmr.khu.ac.ir/article-1-2878-en.html


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Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) Back to browse issues page
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