Let M be an oriented surface and G(2,k) be the Grassmannian.Smooth maps t1 M→G2（2，k) are studied to determine whether or not they are Gauss maps.Some new results have been obtained and some known results reproved.
Gauss maps of oriented timelike 2-surfaces in are characterized, and it is shown that Gallss maps can determine surfaces locally as they do in case. Moreover, some essential differences are discovered between the prop...Gauss maps of oriented timelike 2-surfaces in are characterized, and it is shown that Gallss maps can determine surfaces locally as they do in case. Moreover, some essential differences are discovered between the properties of the Gauss maps of surfaces in Rn and those of the Gauss maps of timelike surfaces in. In particular, a counterexample shows that a nonminimal timelike surface in cannot be essentially determined by its Gauss map.展开更多
文摘Let M be an oriented surface and G(2,k) be the Grassmannian.Smooth maps t1 M→G2（2，k) are studied to determine whether or not they are Gauss maps.Some new results have been obtained and some known results reproved.
文摘Gauss maps of oriented timelike 2-surfaces in are characterized, and it is shown that Gallss maps can determine surfaces locally as they do in case. Moreover, some essential differences are discovered between the properties of the Gauss maps of surfaces in Rn and those of the Gauss maps of timelike surfaces in. In particular, a counterexample shows that a nonminimal timelike surface in cannot be essentially determined by its Gauss map.
