The Almost Hermitian-Einstein Flow

Details The Almost Hermitian-Einstein Flow The Almost Hermitian-Einstein Flow

2006-12-14

arxiv.org/abs/math/0612402v2

Mathematics

Differential Geometry

10 pages

Scientific paper

Let $X$ be a compact K\"ahler manifold, $E\to X$ a Hermitian vector bundle and $L\to X$ an ample line bundle. We construct a non-linear heat flow corresponding to the almost Hermitian-Einstein equation introduced by N.C. Leung, and prove that the solution exists for a short time. We also construct a potential function $D_k$ for this flow. In particular, $D_k$ decreases along the flow.

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