The geometry of hypersurfaces of a Kaehler manifold are studied. Some well-known formulas and theorems in theory of surfaces of Euclidean 3-space are generalized to the hypersurfaces in a Kaehler manifold, such as Gau...The geometry of hypersurfaces of a Kaehler manifold are studied. Some well-known formulas and theorems in theory of surfaces of Euclidean 3-space are generalized to the hypersurfaces in a Kaehler manifold, such as Gauss's formulae, second fundamental form, the equation of Gauss and Codazzi and so forth.展开更多
A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric e...A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly.展开更多
The famous Backlund theorem presented a method to construct a family of surfaces with K=-m^2 from a known surface with K=-m^2, i. e. the well-known Bcklund transformation. With the research and development of the soli...The famous Backlund theorem presented a method to construct a family of surfaces with K=-m^2 from a known surface with K=-m^2, i. e. the well-known Bcklund transformation. With the research and development of the soliton theory, Bcklund transformation has become an important method to find the solutions of soliton equations.At the same time, geometricians also pay attention to generalizing and developing the geometrical content of the Bcklund theorem. In refs. [4] and [5], the authors展开更多
In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation...In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov＇s positive annulus in R^3.展开更多
基金The Project (No.19771068) Supported by the National Science Foundation of China.
文摘The geometry of hypersurfaces of a Kaehler manifold are studied. Some well-known formulas and theorems in theory of surfaces of Euclidean 3-space are generalized to the hypersurfaces in a Kaehler manifold, such as Gauss's formulae, second fundamental form, the equation of Gauss and Codazzi and so forth.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No. ZYGX2010J109)National Natural Science Foundation of China (Grant No. 11101068)the Sichuan Youth Science and Technology Foundation (Grant No. 2011JQ0003)
文摘A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly.
基金the National Natural Science Foundation of China.
文摘The famous Backlund theorem presented a method to construct a family of surfaces with K=-m^2 from a known surface with K=-m^2, i. e. the well-known Bcklund transformation. With the research and development of the soliton theory, Bcklund transformation has become an important method to find the solutions of soliton equations.At the same time, geometricians also pay attention to generalizing and developing the geometrical content of the Bcklund theorem. In refs. [4] and [5], the authors
基金Project supported by the National Natural Science Foundation of China (No. 11101068)the Fundamental Research Funds for the Central Universities (No. ZYGX2010J109)the Sichuan Youth Science and Technology Foundation (No. 2011JQ0003)
文摘In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov＇s positive annulus in R^3.
