强Hamel函数与对称性
Strong Hamel functions and symmetries
AI总结：
本文研究Finsler空间中强Hamel函数与强对偶对称性、强动力学对称性的关系，并证明强Hamel函数可刻画这些对称性，且其射影变形保持χ-曲率。
摘要：
对于Finsler空间的测地喷流，强Hamel函数是一个Hamel函数，它是某个$0$-齐次势函数的测地导数。类似地，强对偶对称性和强动力学对称性分别是与$0$-齐次势函数相关的测地不变的$1$-形式和向量场。我们证明强Hamel函数可以用强对偶对称性和强动力学对称性来刻画。我们表明，通过强Hamel函数的射影变形保持$\chi$-曲率，并分析了与在射影变形下保持曲率张量的其他函数类（Funk函数和弱Funk函数）的关系。
英文摘要：
For the geodesic spray of a Finsler space, a strong Hamel function is a Hamel function that is the geodesic derivative of a $0$-homogeneous potential function. Similarly, strong dual symmetries and strong dynamical symmetries are geodesically invariant $1$-forms and vector fields, respectively, associated with $0$-homogeneous potential functions. We prove that strong Hamel functions can be characterized in terms of strong dual symmetries and strong dynamical symmetries. We show that projective deformations by strong Hamel functions preserve the $χ$-curvature and analyse the relationship with other classes of functions (Funk and weak Funk functions) that preserve the curvature tensors under projective deformations.
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