Some notes on $LP$-Sasakian Manifolds with Generalized Symmetric Metric Connection

Oğuzhan Bahadır; Sudhakar K Chaubey

doi:10.5831/hmj.2020.42.3.461

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arXiv · 1805.00810

Some notes on $LP$-Sasakian Manifolds with Generalized Symmetric Metric Connection

Oğuzhan Bahadır·Sudhakar K Chaubey

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Abstract

The present study initially identify the generalized symmetric connections of type $(\alpha,\beta)$, which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when $(\alpha,\beta)=(1,0)$ and $(\alpha,\beta)=(0,1)$. Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider $CR$-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.

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Oğuzhan Bahadır, Sudhakar K Chaubey. 2018-04-30. Some notes on $LP$-Sasakian Manifolds with Generalized Symmetric Metric Connection. https://doi.org/10.5831/hmj.2020.42.3.461

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