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1
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Einstein-Hermitian and anti-Hermitian 4-manifolds

100%
Jelonek W.
Annales Polonici Mathematici
|
2003
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tom 81
|
nr 1
7-24
EN
We study 4-dimensional Einstein-Hermitian non-Kähler manifolds admitting a certain anti-Hermitian structure. We also describe Einstein 4-manifolds which are of cohomogeneity 1 with respect to an at least 4-dimensional group of isometries.
2
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3-K-contact Wolf spaces

100%
Jelonek W.
Annales Polonici Mathematici
|
2003
|
tom 82
|
nr 2
137-148
EN
The aim of this paper is to give an easy explicit description of 3-K-contact structures on SO(3)-principal fibre bundles over Wolf quaternionic Kähler manifolds.
3
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On almost Kähler type (2G₃) 4-manifolds

100%
Jelonek W.
Colloquium Mathematicum
|
2007
|
tom 108
|
nr 1
19-29
EN
We study four-dimensional almost Kähler manifolds (M,g,J) which satisfy A. Gray's condition (G₃).
4
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On certain four-dimensional almost Kähler manifolds

100%
Jelonek W.
Colloquium Mathematicum
|
2007
|
tom 108
|
nr 1
7-18
EN
We study four-dimensional almost Kähler manifolds (M,g,J) which admit an opposite almost Kähler structure.
5
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QCH Kähler manifolds with κ = 0

100%
Jelonek W.
Colloquium Mathematicum
|
2014
|
tom 136
|
nr 1
31-40
EN
The aim of this paper is to describe all Kähler manifolds with quasi-constant holomorphic sectional curvature with κ = 0.
6
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Homogeneous Riemannian manifolds with generic Ricci tensor

100%
Jelonek W.
Annales Polonici Mathematici
|
2001
|
tom 77
|
nr 3
271-287
EN
We describe homogeneous manifolds with generic Ricci tensor. We also prove that if 𝔤 is a 4-dimensional unimodular Lie algebra such that dim[𝔤,𝔤] ≤ 2 then every left-invariant metric on the Lie group G with Lie algebra 𝔤 admits two mutually opposite compatible left-invariant almost Kähler structures.
7
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Compact holomorphically pseudosymmetric Kähler manifolds

100%
Jelonek W.
Colloquium Mathematicum
|
2009
|
tom 117
|
nr 2
243-249
EN
The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kähler manifolds.
8
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Quaternionic-Kähler geometry and almost Kähler A-manifolds

100%
Jelonek W.
Annales Polonici Mathematici
|
2000
|
tom 75
|
nr 2
111-124
EN
The aim of this paper is to give an easy explicit description of 3-K-contact structures on certain SO(3)-principal fibre bundles over quaternionic-Kähler manifolds.
9
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Affine surfaces with parallel shape operators

100%
Jelonek W.
Annales Polonici Mathematici
|
1991-1992
|
tom 56
|
nr 2
179-186
EN
We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.
10
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Holomorphically pseudosymmetric Kähler metrics on ℂℙⁿ

100%
Jelonek W.
Colloquium Mathematicum
|
2012
|
tom 127
|
nr 1
127-131
EN
The aim of this paper is to present examples of holomorphically pseudosymmetric Kähler metrics on the complex projective spaces ℂℙⁿ, where n ≥ 2.
11
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Toric Hermitian surfaces and almost Kähler structures

100%
Jelonek W.
Annales Polonici Mathematici
|
2007
|
tom 90
|
nr 3
203-217
EN
The aim of this paper is to investigate the class of compact Hermitian surfaces (M,g,J) admitting an action of the 2-torus T² by holomorphic isometries. We prove that if b₁(M) is even and (M,g,J) is locally conformally Kähler and χ(M) ≠ 0 then there exists an open and dense subset U ⊂ M such that $(U,g_{|U})$ is conformally equivalent to a 4-manifold which is almost Kähler in both orientations. We also prove that the class of Calabi Ricci flat Kähler metrics related with the real Monge-Ampère equation is a subclass of the class of Gibbons-Hawking Ricci flat self-dual metrics.
12
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Killing tensors and warped product

100%
Jelonek W.
Annales Polonici Mathematici
|
2000
|
tom 75
|
nr 1
15-33
EN
We present some examples of Killing tensors and give their geometric interpretation. We give new examples of non-compact complete and compact Riemannian manifolds whose Ricci tensor ϱ satisfies the condition $∇_{X} ϱ(X,X) = 2/(n+2) Xτg(X,X)$
13
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Killing tensors and Einstein-Weyl geometry

100%
Jelonek W.
Colloquium Mathematicum
|
1999
|
tom 81
|
nr 1
5-19
EN
We give a description of compact Einstein-Weyl manifolds in terms of Killing tensors.
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