The geometric invariants for mPCLP/mDCLP family

Abstract

The present paper continues our recent works related to the moduli theory of triply periodic minimal surfaces of genus three in terms of three geometric invariants, namely, the Morse index, the nullity, and the signature of a minimal surface. In this paper, we consider mPCLP/mDCLP family, which is listed in Fogden-Hyde [9] and also contains other families in the same paper as its special cases. In fact, the family is a three-parameter family of compact oriented embedded minimal surfaces of genus three in flat three-tori. By numerical arguments, we will compute the three quantities for mPCLP/mDCLP family. Our previous works only treated one-parameter families, and thus the family is of higher dimensional and has richer properties in the moduli space of triply periodic minimal surfaces of genus three.