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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |