S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
Geometric structures modeled after smooth projective horospherical varieties of Picard number one
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- geometric structure; local equivalence; horospherical variety; Cartan geometry; prolongation
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 임선희.
- Geometric 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.