In this paper,we study minimal Legendrian surfacesΣimmersed in the tangent sphere bundle T_(1)R^(3).We classify(1)totally geodesic Legendrian surfaces,(2)closed minimal Legendrian surfaces of genus smaller than or eq...In this paper,we study minimal Legendrian surfacesΣimmersed in the tangent sphere bundle T_(1)R^(3).We classify(1)totally geodesic Legendrian surfaces,(2)closed minimal Legendrian surfaces of genus smaller than or equal to 1 and complete minimal Legendrian surfaces with the non-negative Gauss curvature,and(3)complete stable minimal Legendrian surfaces.展开更多
The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically.Furthermore,an interesting open problem has been proposed in this field.
The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasa...The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasaki) is a Sasakian manifold homothetic with a generalized Berger sphere, and that a natural Cartan structure is arising from the horizontal 1-forms and the author associates a non-Einstein pseudo-Hermitian structure. Also, one studies when the Sasaki type metric of T_1S is generally adapted to the natural co-frame provided by the Finsler structure.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11901534)。
文摘In this paper,we study minimal Legendrian surfacesΣimmersed in the tangent sphere bundle T_(1)R^(3).We classify(1)totally geodesic Legendrian surfaces,(2)closed minimal Legendrian surfaces of genus smaller than or equal to 1 and complete minimal Legendrian surfaces with the non-negative Gauss curvature,and(3)complete stable minimal Legendrian surfaces.
基金supported by Wang KC Foundation of Hong Kongthe National Natural Science Foundation of China.
文摘The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically.Furthermore,an interesting open problem has been proposed in this field.
文摘The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasaki) is a Sasakian manifold homothetic with a generalized Berger sphere, and that a natural Cartan structure is arising from the horizontal 1-forms and the author associates a non-Einstein pseudo-Hermitian structure. Also, one studies when the Sasaki type metric of T_1S is generally adapted to the natural co-frame provided by the Finsler structure.
