A DECOMPOSITION THEOREM FOR IMMERSIONS OF PRODUCT MANIFOLDS

Autor(es)

Tojeiro, Ruy

• Tipo de documento: Artigo Científico
• Fonte: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 59, n. 1, p. 247-269, FEB 2016.
• Citações Web of Science: 2

Resumo

We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally or globally decomposed as a product manifold endowed with a polar metric. For such a product manifold, our main result gives a complete description of all its isometric immersions into a space form whose second fundamental forms are adapted to its product structure in the sense that the tangent spaces to each factor are preserved by all shape operators. This is a far-reaching generalization of a basic decomposition theorem for isometric immersions of Riemannian products due to Moore as well as of its extension by Nolker to isometric immersions of warped products. (AU)

• Processo FAPESP: 11/21362-2 - Ações de grupos, teoria de subvariedades, e análise global em geometria Riemanniana e pseudo-riemanniana
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Temático