Weak equivalence classes of complex vector bundles.
Curvature estimate for the volume growth of globally minimal submanifolds.
Yang-Mills bar connections over compact Kähler manifolds
In this note we introduce a Yang-Mills bar equation on complex vector bundles provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on 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 -form
In this note we prove that any integral closed -form , , on a m-dimensional manifold , , is the restriction of a universal closed -form on a universal manifold as a result of an embedding of to .
Manifolds admitting stable forms
In this note we give a direct method to classify all stable forms on 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.
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