Subvariedades biharmônicas do espaço projetivo quaterniônico - (:unkn) unknown (Universidade Federal do Amazonas, 2019)
The present thesis is devoted to the study of biharmonic submanifolds in quaternionic space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We find the relation between the bitension field of the inclusion of a submanifold in the n-dimensional quaternionic projective space and the bitension field of the inclusion of the corresponding Hopf-tube in the unit sphere of dimension 4n+3. We studied biharmonic with parallel mean curvature and pseudo-umbilicas submanifolds of the projective quaternionic space and we obtained some stability results for this type of submanifold.
Keywords: Fibração de Hopf quaterniônica; Subvariedades biharmônicas; Espaço projetivo quaterniônico; Estimativas de curvatura; Tubo de Hopf; CIÊNCIAS EXATAS E DA TERRA: MATEMÁTICA; Subvariedades biharmônicas; Espaço projetivo quaterniônico; Fibração de Hopf quaterniônica; Estabilidade