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A Closed Form for Slant Submanifolds of Generalized Sasakian Space Forms

Author

Listed:
  • Pablo Alegre

    (Departamento de Economía, Métodos Cuantitativos e Historia Económica. Área de Estadística e Investigación Operativa, Universidad Pablo de Olavide. Ctra. de Utrera, km. 1. 41013 Sevilla, Spain)

  • Joaquín Barrera

    (Department of Geometry and Topology, Faculty of Mathematics, University of Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain)

  • Alfonso Carriazo

    (Department of Geometry and Topology, Faculty of Mathematics, University of Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain
    First and third authors are partially supported by the PAIDI group FQM-327 (Junta de Andalucía, Spain) and the MEC-FEDER grant MTM2011-22621. The third author is member of IMUS (Instituto de Matemáticas de laUniversidda de Sevilla).)

Abstract

The Maslov form is a closed form for a Lagrangian submanifold of C m , and it is a conformal form if and only if M satisfies the equality case of a natural inequality between the norm of the mean curvature and the scalar curvature, and it happens if and only if the second fundamental form satisfies a certain relation. In a previous paper we presented a natural inequality between the norm of the mean curvature and the scalar curvature of slant submanifolds of generalized Sasakian space forms, characterizing the equality case by certain expression of the second fundamental form. In this paper, first, we present an adapted form for slant submanifolds of a generalized Sasakian space form, similar to the Maslov form, that is always closed. And, in the equality case, we studied under which circumstances the given closed form is also conformal.

Suggested Citation

  • Pablo Alegre & Joaquín Barrera & Alfonso Carriazo, 2019. "A Closed Form for Slant Submanifolds of Generalized Sasakian Space Forms," Mathematics, MDPI, vol. 7(12), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1238-:d:297785
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