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Isometric immersions with prefixed second order geometry in minimal codimension

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We analyze the existence of isometric immersions of submanifolds of space forms, preserving the second fundamental form, or a convenient projection of it, into totally geodesic submanifolds of lower dimensions. We characterize some normal fields (that we call Codazzi and Ricci fields) whose global existence ensures such an isometric reduction of the codimension. We relate the existence of these fields to the behaviour of the curvature locus at each point of the submanifold and analyze conditions for the existence of isometric immersions into spheres and the vanishing of the normal curvature.

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Authors and Affiliations

  1. Departament de Geometria i Topologia, Universitat de València, 46100, Burjassot, Valencia, Spain

    María Carmen Romero Fuster

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico D.F, 04510, Mexico

    Federico Sánchez-Bringas

Authors
  1. María Carmen Romero Fuster
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  2. Federico Sánchez-Bringas
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Corresponding author

Correspondence to María Carmen Romero Fuster.

Additional information

M. C. Romero Fuster work was partially supported by DGCYT and FEDER Grant No. MTM2012-33073.

F. Sánchez-Bringas work was partially supported by DGAPA-UNAM: PASPA and PAPIIT-IN117714.

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Romero Fuster, M.C., Sánchez-Bringas, F. Isometric immersions with prefixed second order geometry in minimal codimension. RACSAM 110, 633–654 (2016). https://doi.org/10.1007/s13398-015-0254-2

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  • DOI: https://doi.org/10.1007/s13398-015-0254-2

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