scholarly journals Locally homogeneous rigid geometric structures on surfaces

2011 ◽  
Vol 160 (1) ◽  
pp. 71-90 ◽  
Author(s):  
Sorin Dumitrescu
Keyword(s):  
Geometric Structures ◽  
Locally Homogeneous ◽  
Rigid Geometric Structures

Invariant rigid geometric structures and expanding maps

2011 ◽  
Vol 32 (3) ◽  
pp. 941-959 ◽  
Author(s):  
YONG FANG
Keyword(s):  
Dynamical Systems ◽  
Geometric Structure ◽  
Closed Manifold ◽  
Expanding Maps ◽  
Geometric Structures ◽  
Global Rigidity ◽  
Chaotic Dynamical Systems ◽  
Expanding Map ◽  
Locally Homogeneous ◽  
Rigid Geometric Structures

AbstractIn the first part of this paper, we consider several natural problems about locally homogeneous rigid geometric structures. In particular, we formulate a notion of topological completeness which is adapted to the study of global rigidity of chaotic dynamical systems. In the second part of the paper, we prove the following result: let φ be a C∞ expanding map of a closed manifold. If φ preserves a topologically complete C∞ rigid geometric structure, then φ is C∞ conjugate to an expanding infra-nilendomorphism.

Fujiki class 𝒞 and holomorphic geometric structures

2020 ◽  
Vol 31 (05) ◽  
pp. 2050039
Author(s):  
Indranil Biswas ◽  
Sorin Dumitrescu
Keyword(s):  
Chern Class ◽  
Geometric Structure ◽  
Geometric Structures ◽  
Cartan Geometry ◽  
Compact Torus ◽  
First Chern Class ◽  
Locally Homogeneous ◽  
Simply Connected ◽  
Affine Type ◽  
Compact Complex Manifolds

For compact complex manifolds with vanishing first Chern class that are compact torus principal bundles over Kähler manifolds, we prove that all holomorphic geometric structures on them, of affine type, are locally homogeneous. For a compact simply connected complex manifold in Fujiki class [Formula: see text], whose dimension is strictly larger than the algebraic dimension, we prove that it does not admit any holomorphic rigid geometric structure, and also it does not admit any holomorphic Cartan geometry of algebraic type. We prove that compact complex simply connected manifolds in Fujiki class [Formula: see text] and with vanishing first Chern class do not admit any holomorphic Cartan geometry of algebraic type.

scholarly journals Symmetries of holomorphic geometric structures on tori

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Sorin Dumitrescu ◽  
Benjamin McKay
Keyword(s):  
Homogeneous Space ◽  
Geometric Structure ◽  
Connected Components ◽  
Deformation Space ◽  
Higher Dimension ◽  
Geometric Structures ◽  
Translation Invariant ◽  
Homogeneous Surface ◽  
Complex Torus ◽  
Locally Homogeneous

AbstractWe prove that any holomorphic locally homogeneous geometric structure on a complex torus of dimension two, modelled on a complex homogeneous surface, is translation invariant. We conjecture that this result is true in any dimension. In higher dimension, we prove it for G nilpotent. We also prove that for any given complex algebraic homogeneous space (X, G), the translation invariant (X, G)-structures on tori form a union of connected components in the deformation space of (X, G)-structures.

scholarly journals Holomorphic affine connections on non-Kähler manifolds

2016 ◽  
Vol 27 (11) ◽  
pp. 1650094 ◽  
Author(s):  
Indranil Biswas ◽  
Sorin Dumitrescu
Keyword(s):  
Fundamental Group ◽  
Geometric Structure ◽  
Riemannian Metric ◽  
Complex Manifolds ◽  
Geometric Structures ◽  
Holomorphic Affine ◽  
Locally Homogeneous ◽  
Dimension One ◽  
Affine Type ◽  
Compact Complex Manifolds

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi–Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In particular, if the geometric structure is rigid in Gromov’s sense, then the fundamental group of the manifold must be infinite. We also prove that compact complex manifolds of algebraic dimension one bearing a holomorphic Riemannian metric must have infinite fundamental group.

scholarly journals Invariant Rigid Geometric Structures and Smooth Projective Factors

2009 ◽  
Vol 19 (2) ◽  
pp. 520-535 ◽  
Author(s):  
Amos Nevo ◽  
Robert J. Zimmer
Keyword(s):  
Geometric Structures ◽  
Rigid Geometric Structures
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