Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection

Poyraz, Nergiz (Önen); Yoldaş, Halil İbrahim

doi:10.36890/iejg.545850

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Submanifolds Of Real Space Forms Equipped With a Nonsymmetri...1

Introduction1

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2021

2024

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Cited by 6 publications

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“…Remark 9. N. Poyraz and H. I. Yoldaş derived in [67] the first Chen inequalities for submanifolds of real space forms endowed with a Ricci quarter-symmetric metric connection.…”

Section: Submanifolds Of Real Space Forms Equipped With a Nonsymmetri...mentioning

confidence: 99%

Recent Developments on the First Chen Inequality in Differential Geometry

Chen,

Vîlcu

2023

Mathematics

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One of the most fundamental interests in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of submanifolds and find their applications. In this respect, the first author established, in 1993, a basic inequality involving the first δ-invariant, δ(2), and the squared mean curvature of submanifolds in real space forms, known today as the first Chen inequality or Chen’s first inequality. Since then, there have been many papers dealing with this inequality. The purpose of this article is, thus, to present a comprehensive survey on recent developments on this inequality performed by many geometers during the last three decades.

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“…Remark 9. N. Poyraz and H. I. Yoldaş derived in [67] the first Chen inequalities for submanifolds of real space forms endowed with a Ricci quarter-symmetric metric connection.…”

Section: Submanifolds Of Real Space Forms Equipped With a Nonsymmetri...mentioning

confidence: 99%

Recent Developments on the First Chen Inequality in Differential Geometry

Chen,

Vîlcu

2023

Mathematics

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“…The inequality (1) is known as the Chen-Ricci inequality. This inequality attracted many researchers due to its geometric importance [2][3][4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%