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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohd. Aquib & Michel Nguiffo Boyom & Mohammad Hasan Shahid & Gabriel-Eduard Vîlcu, 2019. "The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms," Mathematics, MDPI, vol. 7(12), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1151-:d:292764
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