Second Variation of F-Einstein-Hilbert Functional

TL;DR

This paper derives a second variation formula for the generalized Einstein-Hilbert functional on Riemannian manifolds, extending the concept of stable Einstein manifolds and exploring their properties.

Contribution

It introduces a new second variation formula for the generalized Einstein-Hilbert functional and extends the definition of stable Einstein manifolds.

Findings

Derived a second variation formula for the functional

Extended the definition of stable Einstein manifolds

Explored properties of these extended stable manifolds

Abstract

This article describes a formula for second variation of generalized Einstein-Hilbert functional on Riemannian manifolds. This work extends the definition of stable Einstein manifolds, and we present some properties.