Spinc Structures on Manifolds and Geometric Applications
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Spinc Structures on Manifolds and Geometric Applications Roger NAKAD April 10, 2012 Max Planck Institute for Mathematics Vivatsgasse 7, 53111 Bonn Germany E-mail: Abstract In this mini-course, we make use of Spinc geometry to study special hyper- surfaces. For this, we begin by selecting basic facts about Spinc structures and the Dirac operator on Riemannian manifolds and their hypersurfaces. We end by giving a Lawson type correspondence for constant mean curvature surfaces in some 3-dimensional Thurston geometries. Contents 1 Introduction and motivations 2 2 Algebraic facts 3 3 Spinc structures and the Dirac operator 5 4 Examples and remarks 8 5 The Schrodinger-Lichnerowicz formula 10 6 Hypersurfaces of Spinc manifolds 12 7 Geometric applications 14 1
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- riemannian manifold
- curvature equal
- dimensional manifold
- mean curvature
- compact riemannian
- manifolds carrying real
- constant mean
SpincStructuresonManifoldsandGeometricApplicationsRogerNAKADApril10,2012MaxPlanckInstituteforMathematicsVivatsgasse7,53111BonnGermanyE-mail:nakad@mpim-bonn.mpg.deAbstractInthismini-course,wemakeuseofSpincgeometrytostudyspecialhyper-surfaces.Forthis,webeginbyselectingbasicfactsaboutSpincstructuresandtheDiracoperatoronRiemannianmanifoldsandtheirhypersurfaces.WeendbygivingaLawsontypecorrespondenceforconstantmeancurvaturesurfacesinsome3-dimensionalThurstongeometries.Contents1Introductionandmotivations2Algebraicfacts3SpincstructuresandtheDiracoperator4Examplesandremarks5TheSchro¨dinger-Lichnerowiczformula6HypersurfacesofSpincmanifolds7Geometricapplications12358012141
