Next Article in Journal
Moving Information Horizon Approach for Dynamic Game Models
Next Article in Special Issue
On Differential Equations Characterizing Legendrian Submanifolds of Sasakian Space Forms
Previous Article in Journal
Application of Differential Evolution Algorithm Based on Mixed Penalty Function Screening Criterion in Imbalanced Data Integration Classification
Previous Article in Special Issue
On the Betti and Tachibana Numbers of Compact Einstein Manifolds
Open AccessArticle

A Closed Form for Slant Submanifolds of Generalized Sasakian Space Forms

1
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
2
Department of Geometry and Topology, Faculty of Mathematics, University of Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain
*
Author to whom correspondence should be addressed.
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).
Mathematics 2019, 7(12), 1238; https://doi.org/10.3390/math7121238
Received: 4 November 2019 / Revised: 7 December 2019 / Accepted: 9 December 2019 / Published: 13 December 2019
(This article belongs to the Special Issue Inequalities in Geometry and Applications)
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. View Full-Text
Keywords: slant submanifolds; generalized Sasakian space forms; closed form; conformal form; Maslov form slant submanifolds; generalized Sasakian space forms; closed form; conformal form; Maslov form
MDPI and ACS Style

Alegre, P.; Barrera, J.; Carriazo, A. A Closed Form for Slant Submanifolds of Generalized Sasakian Space Forms. Mathematics 2019, 7, 1238.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop