The weight Ricci curvature plays an important role in studying global Finsler geometry. In this paper, we study a class of Finsler measure spaces of constant weighted Ricci curvature. We explicitly construct new families of such complete Finsler measure spaces. In particular, we find an eigenfunction and its eigenvalue for such spaces, generalizing a result previously only known in the case of Gaussian shrinking soliton. Finally, we give necessary and sufficient conditions on the coordinate functions for these spaces to be Euclidean measure spaces.
Finsler measure space, constant weighted Ricci curvature, Finsler Gaussian soliton, eigenfunction, eigenvalue
YIN, SONGTING; MO, XIAOHUAN; and ZHU, LING
"A class of Finsler measure spaces of constant weighted Ricci curvature,"
Turkish Journal of Mathematics: Vol. 46:
4, Article 32.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss4/32