PreprintCC BY 4.0arXiv
Geometric Quantities in Spray Geometry and Their Applications to Finsler Geometry
Abstract
In this paper we give an overview of several developments in spray geometry and provide some further interpretations of the geometric quantities that arise naturally in this subject. We discuss, in particular, the S-curvature, the χ-curvature, and several notions of Ricci curvature for sprays. We rederive a number of identities relating these quantities and explain their applications to locally projectively flat sprays and to projectively related sprays. We also discuss applications to Finsler geometry, with emphasis on the χ-curvature of a Finsler metric and on the inverse problem of determining whether a given spray is induced by a Finsler metric.
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BibTeX
@misc{li2026geometric,
title = {{Geometric Quantities in Spray Geometry and Their Applications to Finsler Geometry}},
author = {Benling Li and Zhongmin Shen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31896},
eprint = {2610.31896},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31896},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric Quantities in Spray Geometry and Their Applications to Finsler Geometry
AU - Benling Li
AU - Zhongmin Shen
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31896
UR - https://arxiv.org/abs/2610.31896
AB - In this paper we give an overview of several developments in spray geometry and provide some further interpretations of the geometric quantities that arise naturally in this subject. We discuss, in particular, the S-curvature, the χ-curvature, and several notions of Ricci curvature for sprays. We rederive a number of identities relating these quantities and explain their applications to locally projectively flat sprays and to projectively related sprays. We also discuss applications to Finsler geometry, with emphasis on the χ-curvature of a Finsler metric and on the inverse problem of determining whether a given spray is induced by a Finsler metric.
ER -