The Horizontal Heat Kernel on the Quaternionic Anti-De Sitter Spaces and Related Twistor Spaces

@article{Baudoin2018TheHH,
  title={The Horizontal Heat Kernel on the Quaternionic Anti-De Sitter Spaces and Related Twistor Spaces},
  author={Fabrice Baudoin and Nizar Demni and Jing Wang},
  journal={Potential Analysis},
  year={2018},
  volume={52},
  pages={281-300}
}
The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel formula is explicit enough to derive small time asymptotics. Related twistor spaces and corresponding heat kernels are also discussed. 
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