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• W2950746577 abstract "Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V)-equivariant linear map Pi : wedge^2 W to V. If the skew symmetric vector valued bilinear form Pi is nondegenerate then (M,Q) is endowed with a canonical pseudo-Riemannian metric g such that (M,Q,g) is a homogeneous quaternionic pseudo-Kahler manifold. The construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any spin(V)-equivariant linear map Pi : Sym^2 W to V a homogeneous quaternionic supermanifold (M,Q) is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold (M,Q,g) if the symmetric vector valued bilinear form Pi is nondegenerate." @default.
• W2950746577 created "2019-06-27" @default.
• W2950746577 creator A5079022990 @default.
• W2950746577 date "1999-08-13" @default.
• W2950746577 modified "2023-10-15" @default.
• W2950746577 title "A new construction of homogeneous quaternionic manifolds and related geometric structures" @default.
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