Taiwanese Journal of Mathematics

CERTAIN CLASS OF CONTACT CR-SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE

Hyang Sook Kim and Jin Suk Pak

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Abstract

In this paper we investigate $(n+1)(n \geq 5)$-dimensional contact $CR$-submanifolds $M$ of $(n-1)$ contact $CR$-dimension in a $(2m+1)$-dimensional unit sphere $S^{2m+1}$ which satisfy the condition $h(FX,Y) - h(X,FY) = g(FX,Y) \zeta$ for a normal vector field $\zeta$ 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.

Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 629-646.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405810

Digital Object Identifier
doi:10.11650/twjm/1500405810

Mathematical Reviews number (MathSciNet)
MR2655790

Zentralblatt MATH identifier
1202.53055

Subjects
Primary: 53C40: Global submanifolds [See also 53B25] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
contact $CR$-submanifold odd-dimensional unit sphere Sasakian structure second fundamental form

Citation

Kim, Hyang Sook; Pak, Jin Suk. CERTAIN CLASS OF CONTACT CR-SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE. Taiwanese J. Math. 14 (2010), no. 2, 629--646. doi:10.11650/twjm/1500405810. https://projecteuclid.org/euclid.twjm/1500405810


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References

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