G-variedades riemannianas como hipersuperfícies de formas espaciais.

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

(See full text for download) It is proved that an isometric immersion f: Mn ! Qn+1 c of a compact Riemannian mani-fold of dimension n 3 into a space form of dimension n + 1 is equivariant with respect to a Lie group homomorsm : Iso0(Mn) ! Iso(Qn+1 c ), where Iso0(Mn) denotes the identity component of the isometry group Iso(Mn) of Mn. For the case Qn+1 c = Rn+1, it is shown that takes every closed connected subgroup of Iso(Mn) acting locally polarly on Mn into a group that acts polarly on Rn+1. Moreover, compact Euclidean rotation hypersurfaces of dimension n 3 are characterized by their underlying warped product structure. Besides, isometric immersions f: Mn ! Qn+1 c of a complete Riemannian manifold Mn under a locally polar action of a closed connected subgroup of Iso(Mn) with umbilical principal orbits are studied.

ASSUNTO(S)

ações localmente polares cohomogeneidade hipersuperfícies geometria riemanniana matematica

ACESSO AO ARTIGO

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