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Geometric structures modeled after smooth projective horospherical varieties of Picard number one

DC Field Value Language
dc.contributor.advisor임선희-
dc.contributor.author김신영-
dc.date.accessioned2017-07-14T00:42:25Z-
dc.date.available2017-07-14T00:42:25Z-
dc.date.issued2016-02-
dc.identifier.other000000133390-
dc.identifier.urihttps://hdl.handle.net/10371/121311-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 임선희.-
dc.description.abstractGeometric structures modeled after homogeneous manifolds are studied to
characterize homogeneous manifolds and to prove the deformation rigidity of
them. To generalize these characterizations and deformation rigidity results to
quasihomogeneous manifolds, we first study horospherical varieties and geo
metric structures modeled after horospherical varieties. Using Cartan geom
etry, we prove that a geometric structure modeled after a smooth projective
horospherical variety of Picard number one is locally equivalent to the stan
dard geometric structure when the geometric structure is defined on a Fano
manifold of Picard number one.
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dc.description.tableofcontentsChapter 1 Introduction 1

Chapter 2 Geometric structures on filtered manifolds 6
2.1 G0-structures on filtered manifolds 6
2.2 Prolongations 9
2.3 Cartan connections 11
2.4 Examples 15

Chapter 3 Smooth horospherical varieties of Picard number one 20
3.1 G-varieties 20
3.2 Classifications 22
3.3 Lie algebras of the automorphism groups 26
3.4 Gradations 29
3.5 Varieties of minimal rational tangents 43

Chapter 4 Existence of Cartan connections 50
4.1 Prolongations 50
4.2 Existence of Cartan connections 58
4.3 Geometric structures modeled after horospherical varieties 62

Bibliography 67

국문초록 71
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dc.formatapplication/pdf-
dc.format.extent1249481 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectgeometric structure-
dc.subjectlocal equivalence-
dc.subjecthorospherical variety-
dc.subjectCartan geometry-
dc.subjectprolongation-
dc.subject.ddc510-
dc.titleGeometric structures modeled after smooth projective horospherical varieties of Picard number one-
dc.typeThesis-
dc.description.degreeDoctor-
dc.citation.pages77-
dc.contributor.affiliation자연과학대학 수리과학부-
dc.date.awarded2016-02-
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