Tohoku Mathematical Journal
2024
June
SECOND SERIES VOL. 76, NO. 2

Tohoku Math. J.
76 (2024), 217-227

Title FINSLER WARPED PRODUCT METRICS OF QUADRATIC WEYL CURVATURE

Author Xiaohuan Mo and Hongzhen Zhang

(Received March 23, 2022)
Abstract. The Weyl curvature is one of the most fundamental quantities in projective Finsler geometry. In this paper, we study a class of Finsler warped product metrics with quadratic Weyl curvature. We give necessary and sufficient conditions of such metrics to be of quadratic Weyl curvature which are non-trivial in the sense that these metrics are not of Weyl type, refining a theorem due to Gabrani-Sevim-Shen. As its application, we construct infinitely many new non-trivial W-quadratic Finsler warped product metrics. In particular, we find non-trivial W-quadratic Finsler metrics which are not Douglas type.

Mathematics Subject Classification. Primary 53B40; Secondary 53C60.
Key words and phrases. Finsler manifold, warped product, W-quadratic, scalar curvature, Douglas metric.

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