We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).
@article{bwmeta1.element.bwnjournal-article-apmv69z1p31bwm, author = {Ximin Liu}, title = {Totally real minimal submanifolds in a quaternion projective space}, journal = {Annales Polonici Mathematici}, volume = {69}, year = {1998}, pages = {31-36}, zbl = {0929.53037}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p31bwm} }
Ximin Liu. Totally real minimal submanifolds in a quaternion projective space. Annales Polonici Mathematici, Tome 69 (1998) pp. 31-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p31bwm/
[000] [1] B. Y. Chen and C. S. Houh, Totally real submanifolds of a quaternion projective space, Ann. Mat. Pura Appl. 120 (1979), 185-199. | Zbl 0413.53031
[001] [2] S. Funabashi, Totally real submanifolds of a quaternionic Kaehlerian manifold, Kodai Math. Sem. Rep. 29 (1978), 261-270. | Zbl 0391.53025
[002] [3] S. Ishihara, Quaternion Kählerian manifolds, J. Differential Geom. 9 (1974), 483-500. | Zbl 0297.53014
[003] [4] Y. B. Shen, Totally real minimal submanifolds in a quaternion projective space, Chinese Ann. Math. Ser. B 14 (1993), 297-306. | Zbl 0811.53061
[004] [5] K. Yano, Concircular geometry I, Proc. Imp. Acad. Sci. Japan Tokyo 16 (1940), 195-200.
[005] [6] K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geom. 2 (1968), 161-184. | Zbl 0167.19802