ON THE GEOMETRIC STRUCTURES OF GENERALIZED $(k,\mu)$-SPACE FORMS

Jay Prakash Singh, MOHAN KHATRI

DOI Number
https://doi.org/10.22190/FUMI210613082S
First page
1129
Last page
1142

Abstract


In this paper, the geometric structures of generalized $(k,\mu)$-space forms and their quasi-umbilical hypersurface are analyzed. First $\xi$-$Q$ and conformally flat generalized $(k,\mu)$-space form are investigated and shown that a conformally flat generalized $(k,\mu)$-space form is Sasakian. Next, we prove that a generalized $(k,\mu)$-space form satisfying Ricci pseudosymmetry and $Q$-Ricci pseudosymmetry conditions is $\eta$-Einstein. We obtain the condition under which a quasi-umbilical hypersurface of a generalized $(k,\mu)$-space form is a generalized quasi Einstein hypersurface. Also $\xi$-sectional curvature of a quasi-umbilical hypersurface of generalized $(k,\mu)$-space form is obtained. Finally, the results obtained are verified by constructing an example of 3-dimensional generalized $(k,\mu)$-space form.

Keywords

$(k,\mu)$-space form, Q curvature, Hypersurface, Sasakian, $\eta$-Einstein.

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References


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DOI: https://doi.org/10.22190/FUMI210613082S

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