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On a variational theorem of Gauduchon and torsion-critical manifolds.
- Source :
-
Proceedings of the American Mathematical Society . Apr2023, Vol. 151 Issue 4, p1749-1762. 14p. - Publication Year :
- 2023
-
Abstract
- In 1984, Gauduchon [Math. Ann. 267 (1984), pp. 495–518] considered the functional of L^2-norm of his torsion 1-form on a compact Hermitian manifold. He obtained the Euler-Lagrange equation for this functional, and showed that in dimension 2 the critical metrics must be balanced (namely with vanishing torsion 1-form). In this note we extend his result to higher dimensions, and show that critical metrics are balanced in all dimensions. We also consider the L^2-norm of the full Chern torsion, and show by examples that there are critical points of this functional that are not Kähler. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FUNCTIONAL equations
*LAGRANGE equations
*TORSION
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 151
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 161956696
- Full Text :
- https://doi.org/10.1090/proc/16236