The stability of non-Kähler Calabi-Yau metrics

Abstract

Non Kähler Calabi Yau theory is a newly developed subject and it arises naturally in mathematical physics and generalized geometry. The relevant geometrics are pluriclosed metrics which are critical points of the generalized Einstein Hilbert action. In this work, we study the critical points of the generalized Einstein Hilbert action and discuss the stability of critical points which are defined as pluriclosed steady solitons. We proved that all Bismut Hermitian Einstein manifolds are linearly stable which generalizes the work from Tian, Zhu, Hall, Murphy and Koiso In addition, all Bismut flat pluriclosed steady solitons with positive Ricci curvature are linearly strictly stable.

arXiv commentThis new file corrects the previous errors regarding the convention

References in corpus (7)

• A Gradient Flow for Worldsheet Nonlinear Sigma Models
• On the linear stability of Kähler-Ricci solitons
• The Gibbons-Hawking ansatz in generalized Kähler geometry
• The Stability of Generalized Ricci Solitons
• Variation of complex structures and the stability of Kähler-Ricci Solitons
• Stability and moduli space of generalized Ricci solitons
• Bismut Einstein metrics on compact complex manifolds