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

被引:10
作者
Aquib, Mohd [1 ]
Boyom, Michel Nguiffo [2 ]
Shahid, Mohammad Hasan [1 ]
Vilcu, Gabriel-Eduard [3 ]
机构
[1] Jamia Millia Islamia, Dept Math, Fac Nat Sci, New Delhi 110025, India
[2] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, CC051,Pl E Bataillon, F-34095 Montpellier, France
[3] Petr Gas Univ Ploiesti, Dept Cybernet Econ Informat Finance & Accountancy, Bd Bucuresti 39, Ploiesti 100680, Romania
关键词
Wintgen inequality; generalized complex space form; generalized Sasakian space form; Lagrangian submanifold; Legendrian submanifold; SCALAR CURVATURE CONJECTURE; BI-SLANT SUBMANIFOLDS;
D O I
10.3390/math7121151
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
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页数:20
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