Affine connections on singular multiply warped products and singular twisted products
Siyao Liu, Tong Wu, Yong Wang
TL;DR
This paper extends the study of affine connections to singular multiply warped and twisted products, analyzing their curvature and geometric structures with various connections, and providing illustrative examples.
Contribution
It generalizes previous results to more complex product structures and explores their curvature properties with semi-symmetric connections.
Findings
Curvature formulas for singular multiply warped products
Analysis of Koszul forms and almost product structures
Examples illustrating theoretical results
Abstract
In this paper, we generalize the results in [Y. Wang: Affine connections on singular warped products. Int. J. Geom. Methods Mod. Phys. 18(5), 2150076, (2021).] to singular multiply warped products and singular twisted products. We study singular multiply warped products and singular twisted products and their curvature with the semi-symmetric metric connection and the semi-symmetric non-metric connection. We also discuss Koszul forms associated with the almost product structure and their curvature of singular multiply warped products and singular twisted products. Finally, several examples are presented to demonstrate the theoretical results.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds