1. Blaschke W., "Vorlesungen ϋber Differentialgeometrie II, Affine Differentialgeometrie", Springer, Berlin (1923). ## 2. Farcot E., Gouzé. J. L., "How to control a biological switch: a mathematical framework for the control of piecewise affine models of gene networks", Research Report RR-5979.INRIA Sophia-Antipolis, (2006) 1-8. ## 3. Chen B. Y., "Realization of Robertson-Walker spacetimes as affine hypersurfaces", J. Phy A: Math. Theor., 40 (15) (2007) 4241-4250. ## 4. Amari S., "Differential-Geometrical Methods in Statistics", Lecture Notes in Statistics, Springer, Berlin, Germany, 28(1985). ## 5. Noguchi M., "Geometry of statistical manifolds", Differential Geometry and its Applications 3 (2) (1992) 197-222. ## 6. Netwon N. J, "An infinite-dimensional statistical manifold modelled on Hilbert space", Journal of Functional Analysis, 263 (6) (2012) 1661-1681. ## 7. Dodson C. T. J., "Geometry for stochastically in homogeneous space-times", Non linear Analysis, 47 (2001) 2951-2958. ## 8. Noda T., "Symplectic structures on statistical manifolds", J. Aust. Math. Soc. 90 (2011) 371-384. ## 9. Furuhata H., Hesegawa I., Okuyama Y., Sato K., Shahid M. H., "Sasakian statistical manifolds", Journal of Geometry and Physics, 117, (2017) 179-186. ## 10. Furuhata H., Hesegawa I., Okuyama Y., Sato K., "Kenmotsu Statistical manifolds and warped product", Journal of Geometry, 108 (3) (2017) 1175-1191. ## 11. Furuhata H., "Hypersurfaces in statistical manifolds", Differential Geometry and its Applications, 27 (3) (2009) 420-429. ## 12. Decu S., Haesen S., Verstraelen L., Vilcu G. E., "Curvature invariants of statistical submanifolds in Kenmotsu statistical manifolds of ϕ-sectional curvature", Entropy, 20 (529) (2018) 1-15. ## 13. Casorati F., "Nuova de_nizione della curvatura delle super_cie e suo confront con quella di Gauss (New definition of the curvature of the surface and its comparison with that of Gauss)", Rend. Inst. Matem. Accad. Lomb, Series II, 22 (8) (1889) 335-346. ## 14. Decu S., Haesen S., Verstraelen L., "Optimal inequalities characterising quasi umbilical submanifolds", J. Inequal. Pure. Appl. Math., 9 (2008) 1-7. ## 15. Verstraelen L., "Geometry of submanifolds I, The first Casorati curvature Indicatrices", Kragujev, J. Math., 37 ( 1) (2013) 5-23. MR3073694. ## 16. Kowalczyk D., "Casorati curvatures", Bull, Transilvania Univ., Brasov Ser. III, 1 (50) (2008) 2009-2013. MR2478021 (2009k:53149). ## 17. Lee J. W., Lee C. W., Yoon D. W., "Inequalities for generalized δ-Casorati curvatures of submanifolds in real space forms endowed with a semi-symmetric metric connection", Revista Dela union Matem atica Argentina, 57(2), (2016) 53-62. ## 18. Furuhata H., Hasegawa I., "Submanifold theory in holomorphic statistical manifolds", in: S. Dragomir, M. H. Shahid, F. R. Al-Solamy (Eds.), Geometry of Cauchy-Riemann Submanifolds, Springer, 39 (2016) 179-215. ## 19. Oprea T., "Constrained Extremum Problems in Riemannian Geometry", University of Bucharest Publishing House, Bucharest, Romania, (2006). ## 20. Tripathii M. M., "Inequalities for algebraic Casorati curvatures and their applications", Note di Matematica, 37 (suppl. 1) (2017) 161-186. ## 21. Dillen F., Vrancken L., "Quasi-umbilical.locally strongly convex homogeneous affine hypersurfaces", J. Math. Soc. Jpn., 46 (1994) 477-502. ## 22. Zhang P., Zhang L., "Inequalities for Casorati curvatures of submanifolds in real space forms", Advances in Geometry, 16 (3) (2016) 329-335. ## 23. Hu Z., Li C., Zhang C., "On quasi-umbilical locally strongly convex homogeneous affine hypersurfaces", Differ. Geom. Appl., 33 (2014) 46-74. ## 24. Oguri M., "The classification of 3-dimensional quasi-umbilical locally homogeneous Blaschke hypersurfaces", Differential Geometry and its Applications, 25 (2007) 56-77. ##
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