EUDML

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Yang-Mills bar connections over compact Kähler manifolds

Hông Vân Lê — 2010

Archivum Mathematicum

In this note we introduce a Yang-Mills bar equation on complex vector bundles $E$ provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on $E$ can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among...

Universal spaces for manifolds equipped with an integral closed $k$ -form

Hông-Vân Lê — 2007

Archivum Mathematicum

In this note we prove that any integral closed $k$ -form $φ^{k}$ , $k \geq 3$ , on a m-dimensional manifold $M^{m}$ , $m \geq k$ , is the restriction of a universal closed $k$ -form $h^{k}$ on a universal manifold $U^{d (m, k)}$ as a result of an embedding of $M^{m}$ to $U^{d (m, k)}$ .

Manifolds admitting stable forms

Hông-Van Lê; Martin Panák; Jiří Vanžura — 2008

Commentationes Mathematicae Universitatis Carolinae

In this note we give a direct method to classify all stable forms on $ℝ^{n}$ as well as to determine their automorphism groups. We show that in dimensions 6, 7, 8 stable forms coincide with non-degenerate forms. We present necessary conditions and sufficient conditions for a manifold to admit a stable form. We also discuss rich properties of the geometry of such manifolds.