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

Mohd. Aquib, Michel Nguiffo Boyom, Mohammad Hasan Shahid and Gabriel-Eduard Vîlcu
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Mohd. Aquib: Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi-110025, India
Michel Nguiffo Boyom: Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CC051, Pl. E. Bataillon, F-34095 Montpellier, France
Mohammad Hasan Shahid: Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi-110025, India
Gabriel-Eduard Vîlcu: Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680 Ploieşti, Romania

Mathematics, 2019, vol. 7, issue 12, 1-20

Abstract: 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.

Keywords: Wintgen inequality; generalized complex space form; generalized Sasakian space form; Lagrangian submanifold; Legendrian submanifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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