## Nihonkai Mathematical Journal

- Nihonkai Math. J.
- Volume 28, Number 2 (2017), 89-98.

### The squared chain length function of 5 or 6-membered straight-chains with the tetrahedral bond angle

#### Abstract

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 $n = 5, 6$.

#### Note

The authors would like to express their sincere gratitude to the referee for useful comments. The authors would like to express their sincere gratitude to the editor for valuable help.

#### Article information

**Source**

Nihonkai Math. J., Volume 28, Number 2 (2017), 89-98.

**Dates**

Received: 27 August 2016

First available in Project Euclid: 26 April 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.nihmj/1524708083

**Mathematical Reviews number (MathSciNet)**

MR3794317

**Zentralblatt MATH identifier**

06873761

**Subjects**

Primary: 52C99: None of the above, but in this section

Secondary: 57M50: Geometric structures on low-dimensional manifolds 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

**Keywords**

configuration space molecular structure

#### Citation

Komatsu, Kazushi. The squared chain length function of 5 or 6-membered straight-chains with the tetrahedral bond angle. Nihonkai Math. J. 28 (2017), no. 2, 89--98. https://projecteuclid.org/euclid.nihmj/1524708083