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REEB FLOW INVARIANT UNIT TANGENT SPHERE BUNDLES

Cho, Jong Taek;Chun, Sun Hyang

  • Received : 2014.09.26
  • Accepted : 2014.11.10
  • Published : 2014.12.25

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

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Cited by

  1. Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator vol.6, pp.11, 2018, https://doi.org/10.3390/math6110246