Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule

AUTHOR AND
AFFILIATION

RAFIQUL ISLAM
Department of Mathematics, Jorhat Engineering College, Jorhat-785007 (India)
CHANDRA CHUTIA
Department of Mathematics, Jorhat Institute of Science and Technology, Jorhat (India)

KEYWORDS:

Symmetries, Fuchsian group, Smooth quotient, Riemann surface,

Issue Date:

July 2020

Pages:

88-92

ISSN:

2319-8044 (Online) – 2231-346X (Print)

Source:

Vol.32 – No.7

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DOI:

http://dx.doi.org/10.22147/jusps-A/320701

ABSTRACT:

In this paper, we consider the group of symmetries of the Sulphur molecule (S) which is a finite point group of order 16 denote by D16 generated by two elements having the presentation { u\upsilon/u2\upsilon8 = (u\upsilon)2 = 1} and find the complete set of genera (g ≥ 2) of Compact Riemann surfaces on which  D16 acts as a group of automorphisms as follows:

D16 the group of symmetries of the sulfur (S8) molecule of order 16 acts as an automorphism group of a compact Riemann surfaces of genus g ≥ 2 if and only if there are integers \lambda and \mu such that \lambda \leq 1 and \mu \geq 1 and
g=\lambda +8\mu (\geq2) , \mu\geq |\lambda|

Copy the following to cite this Article:

R. Islam; C. Chutia, “Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule”, Journal of Ultra Scientist of Physical Sciences, Volume 32, Issue 7, Page Number 88-92, 2020


Copy the following to cite this URL:

R. Islam; C. Chutia, “Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule”, Journal of Ultra Scientist of Physical Sciences, Volume 32, Issue 7, Page Number 88-92, 2020

Available from: http://www.ultrascientist.org/paper/1535/