A New Algebraic Inequality and Some Applications in Submanifold Theory

Ion Mihai and Radu-Ioan Mihai
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Ion Mihai: Department of Mathematics, University of Bucharest, 010014 Bucharest, Romania
Radu-Ioan Mihai: Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania

Mathematics, 2021, vol. 9, issue 11, 1-10

Abstract: We give a simple proof of the Chen inequality involving the Chen invariant ? ( k ) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds.

Keywords: Riemannian space form; submanifold; Chen invariants; Chen inequalities; statistical manifold; statistical submanifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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