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Evolution Equations for Non-Degenerate 2-Forms.
- Source :
-
IMRN: International Mathematics Research Notices . Mar2021, Vol. 2021 Issue 6, p4349-4391. 43p. - Publication Year :
- 2021
-
Abstract
- In this paper we introduce several geometric flows that evolve primarily non-degenerate 2-forms, with the motivation to develop a geometric flow to approach the existence of the symplectic forms on a compact manifold that supports a non-degenerate 2-form. In particular, we introduce |$\mathrm{d}^{\ast }\mathrm{d}$| -flow and |$\mathrm{d}^{\ast }\mathrm{d}$| -Ricci flow for a compatible pair |$(\omega , J)$| of an almost Hermitian structure. We prove the short time existence and uniqueness of these flows with smooth initial data, and give some examples of long time existence and convergence. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2021
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 149401791
- Full Text :
- https://doi.org/10.1093/imrn/rny288