Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms
In this article, we derive Chen’s inequalities involving Chen’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariant <inline-formula...
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MDPI AG
2022-07-01
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| author | Yanlin Li Mohan Khatri Jay Prakash Singh Sudhakar K. Chaubey |
| author_facet | Yanlin Li Mohan Khatri Jay Prakash Singh Sudhakar K. Chaubey |
| author_sort | Yanlin Li |
| collection | DOAJ |
| description | In this article, we derive Chen’s inequalities involving Chen’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>M</mi></msub></semantics></math></inline-formula>, Riemannian invariant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>(</mo><msub><mi>m</mi><mn>1</mn></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mi>m</mi><mi>k</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, Ricci curvature, Riemannian invariant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="bold-sans-serif">Θ</mi><mi>k</mi></msub><mrow><mo>(</mo><mn>2</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>m</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms. |
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| last_indexed | 2024-03-09T12:14:58Z |
| publishDate | 2022-07-01 |
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| series | Axioms |
| spelling | doaj.art-8cf816e918ab424b88243ee85e5cb2992023-11-30T22:47:41ZengMDPI AGAxioms2075-16802022-07-0111732410.3390/axioms11070324Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-FormsYanlin Li0Mohan Khatri1Jay Prakash Singh2Sudhakar K. Chaubey3School of Mathematics, Hangzhou Normal University, Hangzhou 311121, ChinaDepartment of Mathematics and Computer Science, Mizoram University, Aizawl 796004, IndiaDepartment of Mathematics and Computer Science, Mizoram University, Aizawl 796004, IndiaDepartment of Information Technology, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, OmanIn this article, we derive Chen’s inequalities involving Chen’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>M</mi></msub></semantics></math></inline-formula>, Riemannian invariant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>(</mo><msub><mi>m</mi><mn>1</mn></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mi>m</mi><mi>k</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, Ricci curvature, Riemannian invariant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="bold-sans-serif">Θ</mi><mi>k</mi></msub><mrow><mo>(</mo><mn>2</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>m</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.https://www.mdpi.com/2075-1680/11/7/324Chen inequalitiesquarter-symmetric connectiongeneralized Sasakian-space-formbi-slantRiemannian invariants |
| spellingShingle | Yanlin Li Mohan Khatri Jay Prakash Singh Sudhakar K. Chaubey Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms Axioms Chen inequalities quarter-symmetric connection generalized Sasakian-space-form bi-slant Riemannian invariants |
| title | Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms |
| title_full | Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms |
| title_fullStr | Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms |
| title_full_unstemmed | Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms |
| title_short | Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms |
| title_sort | improved chen s inequalities for submanifolds of generalized sasakian space forms |
| topic | Chen inequalities quarter-symmetric connection generalized Sasakian-space-form bi-slant Riemannian invariants |
| url | https://www.mdpi.com/2075-1680/11/7/324 |
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