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

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Submanifold Mathematics Space form Space (punctuation) Second fundamental form Pure mathematics Mathematical analysis Type (biology) Complex space Dimension (graph theory) Geometry Mean curvature Curvature Computer science Ecology Affine transformation Biology Operating system

Md Aquib , Michel Nguiffo Boyom , Mohammad Hasan Shahid , Gabriel‐Eduard Vîlcu ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.3390/math7121151 · OA: W2990166978

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.