TY - JOUR
T1 - Some Applications of Casorati Curvature for Statistical Submanifolds of Sasakian Statistical Manifolds and Locally Homogeneous, Quasi-Umbilical Hypersurfaces
TT - کاربردهایی از انحنای کازوراتی برای منیفلدهای آماری و ابررویههای شبه مرکزی همگن
JF - khu-mmr
JO - khu-mmr
VL - 7
IS - 2
UR - http://mmr.khu.ac.ir/article-1-2878-en.html
Y1 - 2021
SP - 215
EP - 236
KW - Statistical manifolds
KW - Sasakian manifolds
KW - Casorati curvature
KW - Local homogeneous
KW - Quasi-umbilical
N2 - 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
M3 10.52547/mmr.7.2.215
ER -