A Closed Form for Slant Submanifolds of Generalized Sasakian Space Forms
| Autor: | Alfonso Carriazo, Pablo Alegre, Joaquín Barrera |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Mean curvature General Mathematics Second fundamental form 010102 general mathematics Space form Conformal map 02 engineering and technology Expression (computer science) Submanifold Space (mathematics) 01 natural sciences slant submanifolds generalized Sasakian space forms closed form conformal form Maslov form 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) 020201 artificial intelligence & image processing Mathematics::Differential Geometry 0101 mathematics Engineering (miscellaneous) Mathematics::Symplectic Geometry Scalar curvature Mathematics |
| Zdroj: | Mathematics; Volume 7; Issue 12; Pages: 1238 |
| ISSN: | 2227-7390 |
| DOI: | 10.3390/math7121238 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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