中心仿射超曲面的若干变分公式
Some Variational Formulae of the Centro-Affine Hypersurfaces
DOI: 10.12677/PM.2021.1112228, PDF,  被引量    国家自然科学基金支持
作者: 王 艳:重庆理工大学理学院,重庆
关键词: 中心仿射超曲面体积变分公式平均曲率Centro-Affine Hypersurfaces Variational Formulae of Volume Mean Curvatures
摘要: 对于仿射空间中的非退化超曲面,运用中心仿射几何量在自然参数下的表示,给出了中心仿射体积的第一和第二变分公式简单的直接证明。进一步研究了Techebychev形式长度平方积分以及3形式长度平方积分的变分公式。
Abstract: The centro-affine differential geometric invariants of a piece of non-degenerate hypersurface in an affine space are represented with respect to the natural parametrization of the given hypersurface. Then a simple and direct proof of the first and the second variation formulae of the centro-affine volume is presented. Furthermore, the variational formulae of the integrals of the square of the length of the Tchebychev field and the cubic form are investigated.
文章引用:王艳. 中心仿射超曲面的若干变分公式[J]. 理论数学, 2021, 11(12): 2048-2056. https://doi.org/10.12677/PM.2021.1112228

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