Abstract
Several relationships between bundle forms of Laguerre planes are found, including the results (1) \({B\mathfrak{B} 0}\), \({D\mathfrak{B}0}\), \({B\mathfrak{B}1^1}\), \({B\mathfrak{B}1^2}\), \({D\mathfrak{B}1}\), \({BD\mathfrak{B}1_{2}}\), \({DD\mathfrak{B}1}\) are equivalent, and (2) \({BD\mathfrak{B}0}\), \({BBD\mathfrak{B}1}\), \({BDD\mathfrak{B}1^1}\), \({BDD\mathfrak{B}1^2}\) are equivalent. A graph indicating all known dependencies between bundle forms in Laguerre planes is provided. It is shown that \({BD\mathfrak{B}2}\) holds in any \({\mathcal{G}}\)-translation Laguerre plane, that is, any Laguerre plane that is a G-translation plane for each parallel class G of spears. A simplified graph of dependencies is supplied for these planes.
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This work was supported by an Ohio University–Chillicothe Summer Research Grant.
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Knight, R.D. Dependencies of bundle forms in Laguerre planes. J. Geom. 106, 123–136 (2015). https://doi.org/10.1007/s00022-014-0239-x
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DOI: https://doi.org/10.1007/s00022-014-0239-x