Spherically symmetric sprays of isotropic curvature

Zuhuan Jia; Benling Li; Zuhuan Jia; Benling Li

doi:10.3934/math.2026932

AIMS Mathematics

2026, Volume 11, Issue 7: 23132-23148. doi: 10.3934/math.2026932

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Research article

Spherically symmetric sprays of isotropic curvature

Zuhuan Jia ,
Benling Li ^,

School of Mathematics and Statistics, Ningbo University, Ningbo, Zhejiang Province 315211, China

Received: 19 May 2026 Revised: 08 July 2026 Accepted: 15 July 2026 Published: 30 July 2026
MSC : 53B40, 53C60

The classification of sprays with isotropic curvature is a central theme in spray geometry. In this paper, we investigated a class of spherically symmetric sprays—those invariant under spherical rotations. First, we derived a necessary and sufficient condition for such a spray to have isotropic curvature; the condition was a system of differential equations. For the important subclass of projectively affine spherically symmetric sprays, we then obtained the corresponding equivalent system of partial differential equations (PDEs). Furthermore, we constructed several explicit sprays of isotropic curvature.
- spray geometry,
- isotropic curvature,
- spherically symmetric spray,
- projectively affine
Citation: Zuhuan Jia, Benling Li. Spherically symmetric sprays of isotropic curvature[J]. AIMS Mathematics, 2026, 11(7): 23132-23148. doi: 10.3934/math.2026932

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Abstract

The classification of sprays with isotropic curvature is a central theme in spray geometry. In this paper, we investigated a class of spherically symmetric sprays—those invariant under spherical rotations. First, we derived a necessary and sufficient condition for such a spray to have isotropic curvature; the condition was a system of differential equations. For the important subclass of projectively affine spherically symmetric sprays, we then obtained the corresponding equivalent system of partial differential equations (PDEs). Furthermore, we constructed several explicit sprays of isotropic curvature.

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