Complex structures on quaternionic manifolds
نویسندگان
چکیده
منابع مشابه
Institute for Mathematical Physics Hypercomplex Structures Associated to Quaternionic Manifolds Hypercomplex Structures Associated to Quaternionic Manifolds
If M is a quaternionic manifold and P is an S 1-instanton over M , then Joyce constructed a hypercomplex manifold we call P (M) over M. These hypercomplex manifolds admit a U(2)-action of a special type permuting the complex structures. We show that up to double covers, all such hypercomplex manifolds arise in this way. Examples, including that of a hypercomplex structure on SU(3), show the nec...
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Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-1 holomorphic sub-bundle D ⊂ TZ which is maximally non-integrable. If Z admits a Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler manifold (M, g). If Z also admits a second complex contact structure D̃ 6= D, then Z = C...
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It has long been known that differential forms on a complex manifold M2n can be decomposed under the action of the complex structure to give the Dolbeault complex. This paper presents an analogous double complex for a quaternionic manifold M4n using the fact that its cotangent space T ∗ mM is isomorphic to the quaternionic vector space H. This defines an action of the group Sp(1) of unit quater...
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Let (M, I, J,K) be a hyperkähler manifold, dimH M = n, and L a non-trivial holomorphic line bundle on (M, I). Using the quaternionic Dolbeault complex, we prove the following vanishing theorem for holomorphic cohomology of L. If c1(L) lies in the closure K̂ of the dual Kähler cone, then H(L) = 0 for i > n. If c1(L) lies in the opposite cone −K̂, then H(L) = 0 for i < n. Finally, if c1(L) is neith...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 1994
ISSN: 0926-2245
DOI: 10.1016/0926-2245(94)00012-3