| SUN HE SHENG.[J].数学年刊A辑,1981,2(2):186~199 |
|
| ON THE PROBLEMS OF THE INFINITESIMALDEFORMATION OF THE SURFACES OFREVOLUTION WITH MIXED CURVATURE |
| Received:November 12, 1979 |
| DOI： |
| 中文关键词: |
| 英文关键词: |
| 基金项目: |
|
| Hits: 576 |
| Download times: 517 |
| 中文摘要: |
| |
| 英文摘要: |
| In this paper the problem of the infinitesimal deformation of the surfaces of revolution with mixed Ganss curvature is studied. In connection with this problem a differential equation of mixed type, which belongs to the second degenerate type, in the form ,
\[k(\rho ){w_{\rho \rho }} + {w_{\theta \theta }} + \rho {w_\rho } = 0({\rho _1} < \rho < {\rho _2},0 \leqslant \theta \leqslant 2\pi )\]
is obtained, where w is the component of the displacement vector of the infinitesimal deformation in the direction of the rotation axis, and\[k(\rho ) = \rho {z^'}(\rho )/{z^{''}}(\rho ),z(\rho )\] being the meridian curve of the surface of revolution.
Suppose a surface of revolution S has two holes \[{L_1}(\rho = {\rho _1})\] and \[{L_2}(\rho = {\rho _2})\], then the meridian of the surface satisfies the condition \[{z^'}(\rho ) = 0\] on \[\rho = {\rho _0}({\rho _1} < {\rho _0} < {\rho _2})\].
If the Gauss curvature K of the surface is a strictly monotone increasing function of \[\rho \], \[{K^'}(\rho ) > 0,{\rho _1} < \rho < {\rho _2}\],then the surface S does not permit of the non-trivial sliding on the plane containing the boundary L2 of the surface. The rigidity of the surface is proved by the energy integral method.
Moreover, the uniqueness of the Tricomi problem, the generalized Tricomi problem, the degenerate Tricomi problem and the Frankl's problem for a piece of surface with mixed curvature are studied. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
