Cantor Laminations and Exceptional Minimal Sets in Codimension One Foliations

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

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Minimal F2-flows

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700022461 ◽

1985 ◽

Vol 39 (2) ◽

pp. 187-193

Author(s):

Daniel Berend

Keyword(s):

Hausdorff Dimension ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Affine Transformations ◽

Dimensional Torus ◽

Minimal Sets ◽

Necessary And Sufficient

AbstractLet σ be an ergodic endomorphism of the r–dimensional torus and Π a semigroup generated by two affine transformations lying above σ. We show that the flow defined by Π admits minimal sets of positive Hausdorff dimension and we give necessary and sufficient conditions for this flow to be minimal.

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Invariant Radon measures and minimal sets for subgroups of Homeo+(R)

Topology and its Applications ◽

10.1016/j.topol.2020.107378 ◽

2020 ◽

Vol 285 ◽

pp. 107378

Author(s):

Hui Xu ◽

Enhui Shi ◽

Yiruo Wang

Keyword(s):

Radon Measures ◽

Minimal Sets

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Affine cones over cubic surfaces are flexible in codimension one

Forum Mathematicum ◽

10.1515/forum-2020-0191 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Alexander Perepechko

Keyword(s):

Automorphism Group ◽

Open Subset ◽

Pezzo Surface ◽

Ample Divisor ◽

Transitive Action ◽

Del Pezzo Surface ◽

Codimension One ◽

Cubic Surfaces ◽

Special Automorphism ◽

Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

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