In this letter we prove several global rigidity theorems for hypersurfaces in Riemannian manifold of constant curvature, which are generalizations of some wellknown theorems for convex hypersurfaces in En+1, Sn+1 and ...In this letter we prove several global rigidity theorems for hypersurfaces in Riemannian manifold of constant curvature, which are generalizations of some wellknown theorems for convex hypersurfaces in En+1, Sn+1 and Hn+1. Our main results are as follows:展开更多
Ⅰ. INTRODUCTIONLet K be a field and F an n×n non-singular alternate matrix over K. From the non-singularity of F, n=2m is even.An n×n matrix P over K is called a symplectie matrix for F if PFP’=F. All the ...Ⅰ. INTRODUCTIONLet K be a field and F an n×n non-singular alternate matrix over K. From the non-singularity of F, n=2m is even.An n×n matrix P over K is called a symplectie matrix for F if PFP’=F. All the symplectic matrices for F form a group with respect to the matrix multiplication. This group is called a symplectic group of degree n defined by F over K and denoted by Sp2m （K, F）. If T is an n×n invertible matrix over K and F=TFT’, then展开更多
Let p be a prime number. The ring B of p-adic integers is the completion ring of a topological ring R_p, where R_p is composed of all rational numbers with its denominator prime to p. In R_p a topological structure is...Let p be a prime number. The ring B of p-adic integers is the completion ring of a topological ring R_p, where R_p is composed of all rational numbers with its denominator prime to p. In R_p a topological structure is defined by p-adic valuation. Similarly, we can define a topology for other subrings of the field Q of rational numbers. Thus some other complete topological rings can be obtained.展开更多
文摘In this letter we prove several global rigidity theorems for hypersurfaces in Riemannian manifold of constant curvature, which are generalizations of some wellknown theorems for convex hypersurfaces in En+1, Sn+1 and Hn+1. Our main results are as follows:
文摘Ⅰ. INTRODUCTIONLet K be a field and F an n×n non-singular alternate matrix over K. From the non-singularity of F, n=2m is even.An n×n matrix P over K is called a symplectie matrix for F if PFP’=F. All the symplectic matrices for F form a group with respect to the matrix multiplication. This group is called a symplectic group of degree n defined by F over K and denoted by Sp2m （K, F）. If T is an n×n invertible matrix over K and F=TFT’, then
文摘Let p be a prime number. The ring B of p-adic integers is the completion ring of a topological ring R_p, where R_p is composed of all rational numbers with its denominator prime to p. In R_p a topological structure is defined by p-adic valuation. Similarly, we can define a topology for other subrings of the field Q of rational numbers. Thus some other complete topological rings can be obtained.
