Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection
The object of this paper is to study invariant submanifolds 𝑀 of Sasakian manifolds 𝑀 admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms 𝜎 and 𝜎 with respect to Levi-Civita connect...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/947640 |
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| author | B. S. Anitha C. S. Bagewadi |
| author_facet | B. S. Anitha C. S. Bagewadi |
| author_sort | B. S. Anitha |
| collection | DOAJ |
| description | The object of this paper is to study invariant submanifolds 𝑀 of Sasakian manifolds 𝑀 admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms 𝜎
and 𝜎 with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form 𝜎 is recurrent, 2-recurrent, generalized 2-recurrent, semiparallel, pseudoparallel, and Ricci-generalized pseudoparallel and M has parallel third fundamental form with respect to semisymmetric nonmetric connection, then M is totally geodesic with respect to Levi-Civita connection. |
| format | Article |
| id | doaj-art-64fe9fafbcc24e34894d7d6580e2066b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-64fe9fafbcc24e34894d7d6580e2066b2025-02-03T01:31:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/947640947640Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric ConnectionB. S. Anitha0C. S. Bagewadi1Department of Mathematics, Kuvempu University, Shankaraghatta, Karnataka, Shimoga 577451, IndiaDepartment of Mathematics, Kuvempu University, Shankaraghatta, Karnataka, Shimoga 577451, IndiaThe object of this paper is to study invariant submanifolds 𝑀 of Sasakian manifolds 𝑀 admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms 𝜎 and 𝜎 with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form 𝜎 is recurrent, 2-recurrent, generalized 2-recurrent, semiparallel, pseudoparallel, and Ricci-generalized pseudoparallel and M has parallel third fundamental form with respect to semisymmetric nonmetric connection, then M is totally geodesic with respect to Levi-Civita connection.http://dx.doi.org/10.1155/2012/947640 |
| spellingShingle | B. S. Anitha C. S. Bagewadi Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection International Journal of Mathematics and Mathematical Sciences |
| title | Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection |
| title_full | Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection |
| title_fullStr | Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection |
| title_full_unstemmed | Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection |
| title_short | Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection |
| title_sort | invariant submanifolds of sasakian manifolds admitting semisymmetric nonmetric connection |
| url | http://dx.doi.org/10.1155/2012/947640 |
| work_keys_str_mv | AT bsanitha invariantsubmanifoldsofsasakianmanifoldsadmittingsemisymmetricnonmetricconnection AT csbagewadi invariantsubmanifoldsofsasakianmanifoldsadmittingsemisymmetricnonmetricconnection |