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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The authors would like to thank Brian Hall for general discussions about complexification of symmetric spaces and the notion of Cartan dual.
Author supported in part by the NSF Grant DMS 1660031
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Baudoin, F., Demni, N. & Wang, J. The Horizontal Heat Kernel on the Quaternionic Anti-De Sitter Spaces and Related Twistor Spaces. Potential Anal 52, 281–300 (2020). https://doi.org/10.1007/s11118-018-9746-y
- Heat kernels
- Subelliptic operators
- Anti-de Sitter spaces
- Symmetric spaces
Mathematics Subject Classification (2010)