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http://dx.doi.org/10.5831/HMJ.2014.36.4.805

REEB FLOW INVARIANT UNIT TANGENT SPHERE BUNDLES

Cho, Jong Taek (Department of Mathematics, Chonnam National University)
Chun, Sun Hyang (Department of Mathematics, Chosun University)

Publication Information

Honam Mathematical Journal / v.36, no.4, 2014 , pp. 805-812 More about this Journal

Abstract

For unit tangent sphere bundles $T_1M$ with the standard contact metric structure ( ${\eta},\bar{g},{\phi},{\xi}$ ), we have two fundamental operators that is, $h=\frac{1}{2}{\pounds}_{\xi}{\phi}$ and ${\ell}=\bar{R}({\cdot},{\xi}){\xi}$ , where ${\pounds}_{\xi}$ denotes Lie differentiation for the Reeb vector field ${\xi}$ and $\bar{R}$ denotes the Riemmannian curvature tensor of $T_1M$ . In this paper, we study the Reeb ow invariancy of the corresponding (0, 2)-tensor fields H and L of h and ${\ell}$ , respectively.

Keywords

unit tangent sphere bundle; contact metric structure; characteristic Jacobi operator;

Citations & Related Records

Reference

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