On applications of Simons’ type formula and reduction of codimension for complete submanifolds in space forms

Autores

  • Kellcio O. Araújo Universidade de Brasília. Departamento de Matemática
  • João Paulo dos Santos Universidade de Brasília. Departamento de Matemática

DOI:

https://doi.org/10.11606/issn.2316-9028.v8i1p95-116

Palavras-chave:

Complete submanifolds, The second fundamental form, Reduction of codimension, Mean curvature

Resumo

We provide a survey of applications of Simons’ type formula to submanifolds with constant mean curvature or with parallel mean curvature vector in Riemannian space forms. Also, we show a result of reduction of codimension for complete submanifolds such that the normalized mean curvature vector is parallel and the squared norm of the second fundamental form satisfies certain inequality. At the end, we give some open questions to submanifolds in general products of Riemannian space forms.

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On applications of Simons’ type formula and reduction of codimension for complete submanifolds in space forms. (2014). São Paulo Journal of Mathematical Sciences, 8(1), 95-116. https://doi.org/10.11606/issn.2316-9028.v8i1p95-116