The total Cartan curvature of Reinhardt surfaces

The Cartan umbilical tensor is a crucial biholomorphic invariant for three-dimensional strictly pseudoconvex CR manifolds. When considering compact manifolds, its L1-norm, referred to as the total Cartan curvature, is an important global numerical invariant. In this study, we seek to calculate the t...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-02, Vol.530 (1), p.127652, Article 127652
Main Author: Son, Duong Ngoc
Format: Article
Language:English
Subjects:
Burns-Epstein invariant
Cartan tensor
Reinhardt boundary
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Summary:The Cartan umbilical tensor is a crucial biholomorphic invariant for three-dimensional strictly pseudoconvex CR manifolds. When considering compact manifolds, its L1-norm, referred to as the total Cartan curvature, is an important global numerical invariant. In this study, we seek to calculate the total Cartan curvature of T3, the three-torus, which features a specific T2-invariant CR structure, incorporating Reinhardt boundaries with closed logarithmic generating curves as a special instance. Our findings present an unexpected corollary indicating that, for many of these boundaries, the total Cartan curvature is equal to 8π2 times the Burns–Epstein invariant.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127652