Abstract
The author shows that if a locally conformal Kähler metric is Hermitian Yang-Mills with respect to itself with Einstein constant c ≤ 0, then it is a Kahler-Einstein metric. In the case of c > 0, some identities on torsions and an inequality on the second Chern number are derived.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Chen, H., Chen, L. and Nie, X., Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metric, Sci. China Math., 64, 2021, 763–780.
Dragomir, S. and Ornea, L., Locally conformal Kähler geometry, Progress in Math., 155, Birkhäuser, 1998.
Gauduchon, P., La 1-forme de torsion d’une variété hermitienne compacte, Math. Ann., 267, 1984, 495–518.
Gauduchon, P. and Ivanov, S., Einstein-Hermitian surfaces and Hermitian Einstein-Weyl structures in dimension 4, Math. Z., 226, 1997, 317–326.
Kobayashi, S., Differential Geometry of Complex Vector Bundles, Iwanami Shoten Publishers and Princeton University Press, Princeton, 1987.
Liu, K. and Yang, X., Geometry of Hermitian manifolds, Internat. J. Math., 23, 2012, 1250055, 40 pp.
Acknowledgement
The author thanks Professor Jixiang Fu for everything.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, J. Locally Conformal Kähler and Hermitian Yang-Mills Metrics. Chin. Ann. Math. Ser. B 42, 511–518 (2021). https://doi.org/10.1007/s11401-021-0274-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11401-021-0274-5