Ehresmann connection for the canonical foliation on a manifold over a local algebra

1996 ◽  
Vol 59 (2) ◽  
pp. 213-218
Author(s):  
V. V. Shurygin
Keyword(s):  
Local Algebra ◽  
Ehresmann Connection ◽  
Canonical Foliation

Multiplicities and Chern Classes in Local Algebra

1998 ◽  
Author(s):  
Paul C. Roberts
Keyword(s):  
Local Algebra ◽  
Chern Classes

Ehresmann connection on manifold foliated by action of noncommutative Lie group

2014 ◽  
Vol 35 (1) ◽  
pp. 43-44
Author(s):  
N. A. Ivanshin
Keyword(s):  
Lie Group ◽  
Ehresmann Connection

scholarly journals Riemannian foliations with Ehresmann connection

2018 ◽  
Vol 20 (4) ◽  
pp. 395-407
Author(s):  
N. I. Zhukova
Keyword(s):  
Linear Connection ◽  
Riemannian Foliation ◽  
Minimal Set ◽  
Foliated Manifold ◽  
Trivial Bundle ◽  
Riemannian Foliations ◽  
Ehresmann Connection ◽  
The Family ◽  
Leaf Space ◽  
Complete Riemannian Manifolds

It is shown that the structural theory of Molino for Riemannian foliations on compact manifolds and complete Riemannian manifolds may be generalized to a Riemannian foliations with Ehresmann connection. Within this generalization there are no restrictions on the codimension of the foliation and on the dimension of the foliated manifold. For a Riemannian foliation (M,F) with Ehresmann connection it is proved that the closure of any leaf forms a minimal set, the family of all such closures forms a singular Riemannian foliation (M,F¯¯¯¯). It is shown that in M there exists a connected open dense F¯¯¯¯-saturated subset M0 such that the induced foliation (M0,F¯¯¯¯|M0) is formed by fibers of a locally trivial bundle over some smooth Hausdorff manifold. The equivalence of some properties of Riemannian foliations (M,F) with Ehresmann connection is proved. In particular, it is shown that the structural Lie algebra of (M,F) is equal to zero if and only if the leaf space of (M,F) is naturally endowed with a smooth orbifold structure. Constructed examples show that for foliations with transversally linear connection and for conformal foliations the similar statements are not true in general.

The analytic algebra associated to a quasi-analytic local algebra

1969 ◽  
Vol 20 (6) ◽  
pp. 612-615
Author(s):  
C. Banica ◽  
O. Stanasila
Keyword(s):  
Local Algebra ◽  
Analytic Algebra

scholarly journals A Remark on Structure of Projective Klingenberg Spaces over a Certain Local Algebra

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 702 ◽  
Author(s):  
Marek Jukl
Keyword(s):  
Local Ring ◽  
Linear Algebra ◽  
Nilpotent Element ◽  
Local Algebra ◽  
Geometric Description

This article is devoted to the projective Klingenberg spaces over a local ring, which is a linear algebra generated by one nilpotent element. In this case, subspaces of such Klingenberg spaces are described. The notion of the “degree of neighborhood” is introduced. Using this, we present the geometric description of subsets of points of a projective Klingenberg space whose arithmetical representatives need not belong to a free submodule.

Review from Local Algebra

2001 ◽  
pp. 141-188
Keyword(s):  
Local Algebra

The local algebra of a map and the Weierstrass preparation theorem

2012 ◽  
pp. 72-83
Author(s):  
V. I. Arnold ◽  
S. M. Gusein-Zade ◽  
A. N. Varchenko
Keyword(s):  
Local Algebra ◽  
Weierstrass Preparation ◽  
Preparation Theorem

Noncommutative local algebra

1994 ◽  
Vol 4 (5) ◽  
pp. 545-585 ◽  
Author(s):  
A. L. Rosenberg
Keyword(s):  
Local Algebra

scholarly journals Dolbeault cohomology of complex manifolds with torus action

2021 ◽  
pp. 173-187
Author(s):  
Roman Krutowski ◽  
Taras Panov
Keyword(s):  
Symmetry Group ◽  
Blow Up ◽  
Hodge Decomposition ◽  
Torus Action ◽  
Cohomology Algebra ◽  
Complex Manifolds ◽  
Dolbeault Cohomology ◽  
Canonical Foliation

We describe the basic Dolbeault cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM- and LVMB-manifolds and, in most generality, complex manifolds with a maximal holomorphic torus action. We also provide a DGA model for the ordinary Dolbeault cohomology algebra. The Hodge decomposition for the basic Dolbeault cohomology is proved by reducing to the transversely Kähler (equivalently, polytopal) case using a foliated analogue of toric blow-up.

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