On the third coefficient in the TYCZ-expansion of the epsilon function of Kaehler-Einstein manifolds

TL;DR

This paper computes the third coefficient in the TYCZ-expansion of the epsilon function for Kähler-Einstein manifolds and explores the implications of this coefficient being zero.

Contribution

It provides the first explicit calculation of the third coefficient in the TYCZ-expansion for Kähler-Einstein metrics and analyzes its geometric significance.

Findings

Explicit expression for the third coefficient in the TYCZ-expansion.

Conditions under which the third coefficient vanishes.

Implications for the geometry of Kähler-Einstein manifolds.

Abstract

In this paper we compute the third coefficient arising from the TYCZ-expansion of the epsilon function associated to a Kaehler-Einstein metric and discuss the consequences of its vanishing.