The natural metric in the Horrocks-Mumford bundle is not Hermitian-Einstein
O. F. B. van Koert, M. Lubke
Abstract
The Horrocks-Mumford bundle E is a famous stable complex vector bundle of rank 2 on 4-dimensional complex projective space. By construction, E has a natural Hermitian metric h1. On the other hand, stability implies the existence of a Hermitian-Einstein metric in E which is unique up to a positive scalar. Now the obvious question is if h1 is in fact the Hermitian-Einstein metric. In this note we indicate how to show by computation that this is not the case.
Create a lesson
Related papers
Uniqueness of Ricci flows from singular initial data
Laura Flower, Man-Chun Lee, Felix Schulze
Generalised Killing Spinors and Euclidean Hypersurfaces
Samuel Forster, Marie-Amélie Lawn
Perelman's entropy and Gromov-Hausdorff versus dynamical stability of round spheres
Reto Buzano, Shengwen Wang
An ambient metric framework for sharp compactness of the constant Q2N-curvature problem
Liuwei Gong, Seunghyeok Kim, Juncheng Wei
Rigidity of Ricci solitons for φ-related metallic semi-Riemannian structures on para-Kenmotsu manifolds
Yasemin Karababa
On isotropic points and contact invariants of curves
Amanda Dias Falqueto, Juan J. Nuño Ballesteros, Raúl Oset Sinha