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Open AccessArticle

The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms

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Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi-110025, India
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Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CC051, Pl. E. Bataillon, F-34095 Montpellier, France
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Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680 Ploieşti, Romania
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1151; https://doi.org/10.3390/math7121151
Received: 23 October 2019 / Revised: 24 November 2019 / Accepted: 25 November 2019 / Published: 1 December 2019
(This article belongs to the Special Issue Inequalities in Geometry and Applications)
In this work, we first derive a generalized Wintgen type inequality for a Lagrangian submanifold in a generalized complex space form. Further, we extend this inequality to the case of bi-slant submanifolds in generalized complex and generalized Sasakian space forms and derive some applications in various slant cases. Finally, we obtain obstructions to the existence of non-flat generalized complex space forms and non-flat generalized Sasakian space forms in terms of dimension of the vector space of solutions to the first fundamental equation on such spaces. View Full-Text
Keywords: Wintgen inequality; generalized complex space form; generalized Sasakian space form; Lagrangian submanifold; Legendrian submanifold Wintgen inequality; generalized complex space form; generalized Sasakian space form; Lagrangian submanifold; Legendrian submanifold
MDPI and ACS Style

Aquib, M.; Boyom, M.N.; Shahid, M.H.; Vîlcu, G.-E. The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms. Mathematics 2019, 7, 1151.

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