Abstract
In this paper, we establish an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds by using the Mathai-Quillen’s superconnection formalism, in which no extra vector field is involved. Furthermore, we prove a more general Lichnerowicz formula in this direction through a geometric localization procedure.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11221091, 11271062, 11501067, 11571184, 11871126 and 11931007), Natural Science Foundation of Chongqing, China (Grant No. CSTB2022NSCQ-MSX0397), the Fundamental Research Funds for the Central Universities and Nankai Zhide Foundation, and the Chern Institute of Mathematics Visiting Scholars Program. The authors thank Professor Weiping Zhang for his generosity in sharing his ideas on this problem with us as well as for his encouragement.
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Dedicated to Professor Shiing-Shen Chern and Professor Yibing Shen
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Feng, H., Li, M. Superconnections and an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds. Sci. China Math. 66, 1903–1932 (2023). https://doi.org/10.1007/s11425-023-2144-6
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DOI: https://doi.org/10.1007/s11425-023-2144-6