Komatsu, Kazushi The squared chain length function of 5 or 6-membered straight-chains with the tetrahedral bond angle. (English) Zbl 1390.52027 Nihonkai Math. J. 28, No. 2, 89-98 (2017). Summary: We provide straight-chains with the tetrahedral bond angle \(\cos^{-1}(-1/3)\) as a mathematical model of \(n\)-membered straight-chain hydrocarbon molecules. We study the squared chain length function on the configuration space of the model and determine the critical points with planar configurations when \(n=5,6\). Cited in 1 Document MSC: 52C99 Discrete geometry 57M50 General geometric structures on low-dimensional manifolds 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) Keywords:configuration space; molecular structure × Cite Format Result Cite Review PDF Full Text: Euclid References: [1] S. Goto and K. Komatsu, The configuration space of a model for ringed hydrocarbon molecules, Hiroshima Math. J. 42 (2012), 115-126. · Zbl 1238.92069 [2] S. Goto, K. Komatsu and J. Yagi, A remark on the configuration space of a model for ringed hydrocarbon molecules, Kochi J. Math. 7 (2012), 1-15. · Zbl 1271.92043 [3] S. Goto, K. Komatsu and J. Yagi, The configuration space of a model for 5-membered straight-chain hydrocarbon molecules parametrized by chain lengths, Nihonkai Math. J. 26 (2015), 37-45. · Zbl 1338.92149 [4] H. Kamiya, Weighted trace functions as examples of Morse functions, J. Fac. Sci. Shinshu Univ. 6 (1971), 85-96. · Zbl 0322.58006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.