Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection
Purpose – In 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Di...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2025-01-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2021-0057/full/pdf |
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| author | Mohd Aslam Mohd Danish Siddiqi Aliya Naaz Siddiqui |
| author_facet | Mohd Aslam Mohd Danish Siddiqi Aliya Naaz Siddiqui |
| author_sort | Mohd Aslam |
| collection | DOAJ |
| description | Purpose – In 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken gave a conjecture of Wintgen inequality, named as the DDVV-conjecture, for general Riemannian submanifolds in real space forms. Later on, this conjecture was proven to be true by Z. Lu and by Ge and Z. Tang independently. Since then, the study of Wintgen’s inequalities and Wintgen ideal submanifolds has attracted many researchers, and a lot of interesting results have been found during the last 15 years. The main purpose of this paper is to extend this conjecture of Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection. Design/methodology/approach – The authors used standard technique for obtaining generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection. Findings – The authors establish the generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection, and also find conditions under which the equality holds. Some particular cases are also stated. Originality/value – The research may be a challenge for new developments focused on new relationships in terms of various invariants, for different types of submanifolds in that ambient space with several connections. |
| format | Article |
| id | doaj-art-2c0531c602654e729f2f933132fba687 |
| institution | Kabale University |
| issn | 1319-5166 2588-9214 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj-art-2c0531c602654e729f2f933132fba6872025-01-24T04:22:17ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142025-01-0131122110.1108/AJMS-03-2021-0057Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connectionMohd Aslam0Mohd Danish Siddiqi1Aliya Naaz Siddiqui2Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi, IndiaDepartment of Mathematics, Jazan University, Jazan, Saudi ArabiaDepartment of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana-Ambala, IndiaPurpose – In 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken gave a conjecture of Wintgen inequality, named as the DDVV-conjecture, for general Riemannian submanifolds in real space forms. Later on, this conjecture was proven to be true by Z. Lu and by Ge and Z. Tang independently. Since then, the study of Wintgen’s inequalities and Wintgen ideal submanifolds has attracted many researchers, and a lot of interesting results have been found during the last 15 years. The main purpose of this paper is to extend this conjecture of Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection. Design/methodology/approach – The authors used standard technique for obtaining generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection. Findings – The authors establish the generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection, and also find conditions under which the equality holds. Some particular cases are also stated. Originality/value – The research may be a challenge for new developments focused on new relationships in terms of various invariants, for different types of submanifolds in that ambient space with several connections.https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2021-0057/full/pdfNormalized scalar curvatureScalar curvatureMean curvatureQuarter-symmetric connectionConformal Sasakian space form |
| spellingShingle | Mohd Aslam Mohd Danish Siddiqi Aliya Naaz Siddiqui Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection Arab Journal of Mathematical Sciences Normalized scalar curvature Scalar curvature Mean curvature Quarter-symmetric connection Conformal Sasakian space form |
| title | Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection |
| title_full | Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection |
| title_fullStr | Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection |
| title_full_unstemmed | Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection |
| title_short | Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection |
| title_sort | generalized wintgen inequality for bi slant submanifolds in conformal sasakian space form with quarter symmetric connection |
| topic | Normalized scalar curvature Scalar curvature Mean curvature Quarter-symmetric connection Conformal Sasakian space form |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2021-0057/full/pdf |
| work_keys_str_mv | AT mohdaslam generalizedwintgeninequalityforbislantsubmanifoldsinconformalsasakianspaceformwithquartersymmetricconnection AT mohddanishsiddiqi generalizedwintgeninequalityforbislantsubmanifoldsinconformalsasakianspaceformwithquartersymmetricconnection AT aliyanaazsiddiqui generalizedwintgeninequalityforbislantsubmanifoldsinconformalsasakianspaceformwithquartersymmetricconnection |