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 ...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.展开更多
In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifo...In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifolds of dimension n 4 with vanishing Landsberg curvatures must be Berwald manifolds.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11221091,11271062,11501067,11571184,11871126 and 11931007)Natural Science Foundation of Chongqing+2 种基金China(Grant No.CSTB2022NSCQ-MSX0397)the Fundamental Research Funds for the Central Universities and Nankai Zhide Foundationthe Chern Institute of Mathematics Visiting Scholars Program。
文摘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.
基金supported by National Natural Science Foundation of China (Grant Nos. 11221091, 11271062, 11501067, 11571184, 11871126 and 11931007)China Scholarship Council Visiting Scholar Program+1 种基金the Fundamental Research Funds for the General UniversitiesNankai Zhide Foundation。
文摘In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifolds of dimension n 4 with vanishing Landsberg curvatures must be Berwald manifolds.
