The Dirac operator on locally reducible Riemannian manifolds

Abstract

In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in the sense that, for the first eigenvalue, they reduce to the result [1] of Alexandrov.

A Kastler–Kalau–Walze Type Theorem for the J-Twist $$D_{J}$$ of the Dirac Operator

“…Kim had given some preliminaries and lemmas about the Dirac operator D and the J-twist in [18]. In [19,20], the author checked that D J is a formally self-adjoint elliptic operator. By simple calculations, the leading symbol of the J-twist D J of the Dirac operator is not √ −1c(ξ).…”

A Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator

“…On the other hand, some preliminaries and lemmas about the Dirac operator D and the J-twist are given in [18]. In [19,20], the author got estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds by the J-twist of the Dirac operator. It can be obtained by simple calculations that the leading symbol of the J-twist D J of the Dirac operator is not √ −1c(ξ).…”

Dirac Equation for Posch-Teller Potential in Radial Section Symmetry Spin Case using Asymptotic Iteration Method

“…Alam et al, 2016) whose potential energy is a function of position(S. M. Ikhdair, Hamzavi, & Rajabi, 2013). The solution to the Dirac (Chen, 2019) equation can be solved by reducing the Dirac equation to a Second Order Differential equation.…”