Spin c Manifolds and Complex Contact Structures
Copyright policy )Spin c Manifolds and Complex Contact Structures
The author extends the notion of a projectable spinor on a spin manifold to a manifold with \(\text{Spin}^c\) structure and shows relations of spinors on the base and on the total space of a Riemannian submersion with totally geodesic one-dimensional fibres. As an application, it is shown that a compact Kähler manifold \(M\) of positive scalar curvature and complex dimension \(4m+3\) is a twistor space of a quaternionic Kähler manifold if and only if \(M\) is Kähler-Einstein and admits a complex contact structure.
- Humboldt-Universität zu Berlin Germany
- École Polytechnique France
quaternionic Kähler manifold, Spin\(^c\) manifold, Spectral problems; spectral geometry; scattering theory on manifolds, Spin and Spin\({}^c\) geometry, Global differential geometry of Hermitian and Kählerian manifolds, complex contact structure, projectable spinor, twistor space, Specialized structures on manifolds (spin manifolds, framed manifolds, etc.), 510, Special Riemannian manifolds (Einstein, Sasakian, etc.), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], General geometric structures on manifolds (almost complex, almost product structures, etc.)
quaternionic Kähler manifold, Spin\(^c\) manifold, Spectral problems; spectral geometry; scattering theory on manifolds, Spin and Spin\({}^c\) geometry, Global differential geometry of Hermitian and Kählerian manifolds, complex contact structure, projectable spinor, twistor space, Specialized structures on manifolds (spin manifolds, framed manifolds, etc.), 510, Special Riemannian manifolds (Einstein, Sasakian, etc.), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], General geometric structures on manifolds (almost complex, almost product structures, etc.)
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