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Search Results: 1 - 10 of 7954 matches for " Benjamin McKay "
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Extension Phenomena for Holomorphic Geometric Structures
Benjamin McKay
Symmetry, Integrability and Geometry : Methods and Applications , 2009,
Abstract: The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.
Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
Benjamin McKay
Symmetry, Integrability and Geometry : Methods and Applications , 2011,
Abstract: We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact K hler manifolds.
G2 manifolds of cohomogeneity two
Benjamin McKay
Mathematics , 2003,
Abstract: This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.
Rigid geometry on projective varieties
Benjamin McKay
Mathematics , 2006,
Abstract: We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.
Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
Benjamin McKay
Mathematics , 2008, DOI: 10.3842/SIGMA.2011.090
Abstract: We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact K\"ahler manifolds.
Extension Phenomena for Holomorphic Geometric Structures
Benjamin McKay
Mathematics , 2008, DOI: 10.3842/SIGMA.2009.058
Abstract: The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.
Lifting locally homogeneous geometric structures
Benjamin McKay
Mathematics , 2011,
Abstract: We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.
Morphisms of Cartan connections
Benjamin McKay
Mathematics , 2008,
Abstract: We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We prove some basic results concerning completeness of Cartan connections. We provide a new method to prove completeness of Cartan connections using families of morphisms.
The Hartogs extension phenomenon for holomorphic parabolic and reductive geometries
Benjamin McKay
Mathematics , 2013,
Abstract: Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my paper [14]. We use this result to classify the Hopf manifolds which admit holomorphic reductive geometries, and to classify the Hopf manifolds which admit holomorphic parabolic geometries. Every Hopf manifold which admits a holomorphic parabolic geometry with a given model admits a flat one. We classify flat holomorphic parabolic geometries on Hopf manifolds.
Summary of progress on the Blaschke conjecture
Benjamin McKay
Mathematics , 2013,
Abstract: The Blaschke conjecture claims that every compact Riemannian manifold whose injectivity radius equals its diameter is, up to constant rescaling, a compact rank one symmetric space. We summarize the intuition behind this problem, the proof that such manifolds have the cohomology of compact rank one symmetric spaces, and the proof of the conjecture for homology spheres and homology real projective spaces. We also summarize what is known on the diffeomorphism, homeomorphism and homotopy types of such manifolds.
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