Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in Funk spaces has at most two distinct principal curvatures....Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in Funk spaces has at most two distinct principal curvatures. Moreover, a complete classification of isoparametric families in a Funk space is given.展开更多
In this paper,we study the growth of fundamental groups of Finsler manifolds.Some relationships between the growth of fundamental groups and the volume growth of universal covers of Finsler manifolds are found.Some es...In this paper,we study the growth of fundamental groups of Finsler manifolds.Some relationships between the growth of fundamental groups and the volume growth of universal covers of Finsler manifolds are found.Some estimates of entropies and the number of generators of fundamental groups of Finsler manifolds are given.Moreover,the quasi-isometry and the geometric norm in Finsler geometry are considered.展开更多
We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(r...We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(resp.a segment).Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated.These generalize the corresponding results in recent literature.展开更多
By using Darboux transformations, the authors give the explicit construction for local iso-metric immersions of space forms Mn(c) into space forms M2n-1(c + ε2) via purely algebraicalgorithm.
In terms of the almost complex connection and the unitary moving frame, a complex version on the theory of the nearly Khler structure in S^(6) is given. Under this framework, minimal surfaces in the nearly Khler...In terms of the almost complex connection and the unitary moving frame, a complex version on the theory of the nearly Khler structure in S^(6) is given. Under this framework, minimal surfaces in the nearly Khler S^(6) are studied. A complete classification for c omplete minimal surfaces in S^(6) with constant Khler angle and nonnegative curvature is given. Moreover, almost complex curves in S^(6) are considered.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11471246)Anhui Provincial Natural Science Foundation (Grant No. 1608085MA03)Natural Science Foundation of Higher Education in Anhui Province (Grant No. KJ2014A257)
文摘Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in Funk spaces has at most two distinct principal curvatures. Moreover, a complete classification of isoparametric families in a Funk space is given.
基金supported by National Natural Science Foundation of China (Grant No.10871171)
文摘In this paper,we study the growth of fundamental groups of Finsler manifolds.Some relationships between the growth of fundamental groups and the volume growth of universal covers of Finsler manifolds are found.Some estimates of entropies and the number of generators of fundamental groups of Finsler manifolds are given.Moreover,the quasi-isometry and the geometric norm in Finsler geometry are considered.
基金supported by National Natural Science Foundation of China(Grant No.11171253)the Natural Science Foundation of Ministry of Education of Anhui Province(Grant No.KJ2012B197)
文摘We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(resp.a segment).Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated.These generalize the corresponding results in recent literature.
基金Project supported by the National Natural Science Foundation of China (No.10271106)the Science Foundation of the Ministry of Education of Chinathe Natural Science Foundation of Zhejiang Province, China.
文摘By using Darboux transformations, the authors give the explicit construction for local iso-metric immersions of space forms Mn(c) into space forms M2n-1(c + ε2) via purely algebraicalgorithm.
文摘In terms of the almost complex connection and the unitary moving frame, a complex version on the theory of the nearly Khler structure in S^(6) is given. Under this framework, minimal surfaces in the nearly Khler S^(6) are studied. A complete classification for c omplete minimal surfaces in S^(6) with constant Khler angle and nonnegative curvature is given. Moreover, almost complex curves in S^(6) are considered.
