arXiv subjects
Publications and source records attributed to Robin S. Krom.
This is an exposition of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The original work appeared in [1].
The Donaldson metric is a metric on the space of symplectic two-forms in a fixed cohomology class. It was introduced in [2]. We compute the associated Levi-Civita connection, describe it's geodesics and compute the formula for the covariant Hessian of an energy functional on the space of symplectic structures in a fixed cohomology class, introduced by S.Donaldson in [1].
We prove the local existence of unique smooth solutions of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. It is a semiflow on the Besov space $B^{1,p}_2(M, Λ^2)$ for $p > 4$. The Donaldson geometric flow was introduced by Simon Donaldson in [2]. For a detailed exposition see [6].