Huiyang XU , Cece LI . CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM^*[J]. Acta mathematica scientia, Series B, 2023 , 43(6) : 2413 -2429 . DOI: 10.1007/s10473-023-0606-5

[1] Antić M, Dillen F, Schoels K, et al. Decomposable affine hypersurfaces. Kyushu J Math, 2014, 68: 93-103
[2] Antić M, Hu Z, Li C, et al. Characterization of the generalized Calabi composition of affine hyperspheres. Acta Math Sin (Engl Ser), 2015, 31: 1531-1554
[3] Antić M, Li H, Vrancken L, et al. Affine hypersurfaces with constant sectional curvature. Pacific J Math, 2021, 310: 275-302
[4] Birembaux O, Djorić M.Isotropic affine spheres. Acta Math Sin (Engl Ser), 2012, 28: 1955-1972
[5] Brozos-Vázquez M, García-Ró E, Vázquez-Lorenzo R. Complete locally conformally flat manifolds of negative curvature. Pacific J Math, 2006, 226: 201-219
[6] Bokan N, Nomizu K, Simon U. Affine hypersurfaces with parallel cubic forms. Tôhoku Math J, 1990, 42: 101-108
[7] Birembaux O, Vrancken L. Isotropic affine hypersurfaces of dimension $5$. J Math Anal Appl, 2014, 417: 918-962
[8] Calabi E. Complete affine hyperspheres, I. Sympos Math, 1972, 10: 19-38
[9] Cheng X, Hu Z. On the isolation phenomena of locally conformally flat manifolds with constant scalar curvature-submanifolds versions. J Math Anal Appl, 2018, 464: 1147-1157
[10] Dillen F, Vrancken L. 3-dimensional affine hypersurfaces in $\mathbb{R}^4$ with parallel cubic form. Nagoya Math J, 1991, 124: 41-53
[11] Dillen F, Vrancken L. Calabi-type composition of affine spheres. Differ Geom Appl, 1994, 4: 303-328
[12] Dillen F, Vrancken L. Hypersurfaces with parallel difference tensor. Japan J Math, 1998, 24: 43-60
[13] Dillen F, Vrancken L, Yaprak S. Affine hypersurfaces with parallel cubic form. Nagoya Math J, 1994, 135: 153-164
[14] Gigena S. Inductive schemes for the complete classification of affine hypersurfaces with parallel second fundamental form. Beitr Algebra Geom, 2011, 52: 51-73
[15] Hildebrand R. Graph immersions with parallel cubic form. Differ Geom Appl, 2021, 74: 101700
[16] Hu Z, Li C, Li H, et al. Lorentzian affine hypersurfaces with parallel cubic form. Results Math, 2011, 59: 577-620
[17] Hu Z, Li C, Li H, et al.The classification of 4-dimensional non-degenerate affine hypersurfaces with parallel cubic form. J Geom Phys, 2011, 61: 2035-2057
[18] Hu Z, Li H, Simon U, et al. On locally strongly convex affine hypersurfaces with parallel cubic form. Part I. Differ Geom Appl, 2009, 27: 188-205
[19] Hu Z, Li H, Vrancken L. Characterizations of the Calabi product of hyperbolic affine hyperspheres. Results Math, 2008, 52: 299-314
[20] Hu Z, Li H, Vrancken L. Locally strongly convex affine hypersurfaces with parallel cubic form. J Differ Geom, 2011, 87: 239-307
[21] Hu Z, Xing C. New equiaffine characterizations of the ellipsoids related to an equiaffine integral inequality on hyperovaloids. Math Inequal Appl, 2021, 24: 337-350
[22] Hu Z, Yin J. Equivariant minimal immersions from $S^3$ into $\mathbb{C}P^3$. Acta Math Sci, 2019, 39B(4): 1065-1080
[23] Li A-M, Simon U, Zhao G, et al.Global Affine Differential Geometry of Hypersurfaces. 2nd ed. Berlin/Boston: Walter de Gruyter, 2015
[24] Li C, Xing C, Xu H. Locally strongly convex affine hypersurfaces with semi-parallel cubic form. J Geom Anal, 2023, 33: 81
[25] Magid M, Nomizu K. On affine surfaces whose cubic forms are parallel relative to the affine metric. Proc Japan Acad (Ser A), 1989, 65: 215-218
[26] Nomizu K, Sasaki T.Affine Differential Geometry: Geometry of Affine Immersions. Cambridge: Cambridge University Press, 1994
[27] Opozda B. Some inequalities and applications of Simons' type formulas in Riemannian, affine,statistical geometry. J Geom Anal, 2022, 32: 108
[28] Vrancken L, Li A-M, Simon U. Affine spheres with constant affine sectional curvature. Math Z, 1991, 206: 651-658
[29] Wang C P. Canonical equiaffine hypersurfaces in $\mathbb{R}^{n+1}$. Math Z, 1993, 214: 579-592
[30] Xu R, Lei M. Classification of Calabi hypersurfaces in $\mathbb{R}^{5}$ with parallel Fubini-Pick form. Acta Math Sci, 2022, 42A(2): 321-337