Some Pinching Results for Bi-Slant Submanifolds in S -Space Forms

Mohd Aquib, Meraj Ali Khan, Adela Mihai and Ion Mihai
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Mohd Aquib: Department of Mathematics, Sri Venkateswara College, University of Delhi, New Delhi-110021, India
Meraj Ali Khan: Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
Adela Mihai: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania
Ion Mihai: Department of Mathematics, University of Bucharest, 010014 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 9, 1-18

Abstract: The objective of the present article is to prove two geometric inequalities for submanifolds in S -space forms. First, we establish inequalities for the generalized normalized δ -Casorati curvatures for bi-slant submanifolds in S -space forms and then we derive the generalized Wintgen inequality for Legendrian and bi-slant submanifolds in the same ambient space. We also discuss the equality cases of the inequalities. Further, we provide some immediate geometric applications of the results. Finally, we construct some examples of slant and Legendrian submanifolds, respectively.

Keywords: bi-slant submanifolds; Casorati curvature; Wintgen inequality; S -space forms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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