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Commun. Korean Math. Soc. 2014; 29(1): 131-140

Printed January 31, 2014

https://doi.org/10.4134/CKMS.2014.29.1.131

Copyright © The Korean Mathematical Society.

Certain class of contact $CR$-submanifolds of a Sasakian space form

Hyang Sook Kim, Don Kwon Choi, and Jin Suk Pak

Inje University, Kyungpook National University, Kyungpook National University

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In this paper we investigate $(n+1)(n\geq 3)$-dimensional contact $CR$-submanifolds $M$ of $(n-1)$ contact $CR$-dimension in a complete simply connected Sasakian space form of constant $\phi$-holomorphic sectional curvature $c\not= -3$ which satisfy the condition $ h(FX,Y)+h(X,FY)$ $=0$ for any vector fields $X, Y$ tangent to $M$, where $h$ and $F$ denote the second fundamental form and a skew-symmetric endomorphism (defined by (2.3)) acting on tangent space of $M$, respectively.

Keywords: contact $CR$-submanifold, Sasakian space form, almost contact structure, Sasakian structure, second fundamental form

MSC numbers: 53C40, 53C25

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