Abstract
In this paper, we introduce a curve shortening flow in a 3-dimensional pseudohermitian manifold with vanishing torsion. The flow preserves the Legendrian condition and decreases the length of curves. The stationary solution of our flow is a Legendrian geodesic. We classify the singularity and prove some convergence results. Moreover, we study the flow in Heisenberg group especially with Type I singularity.
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Acknowledgements
The authors would like to thank Professor Jiayu Li for his constant support. S. Pan is support by NSFC 11721101, National Key Research and Development Project SQ2020YFA070080. J. Sun is support by NSFC 12071352.
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Communicated by J. Jost.
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