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Killing tensors and Einstein-Weyl geometry

100%

Jelonek W.

Colloquium Mathematicum

1999

tom 81

nr 1

5-19

We give a description of compact Einstein-Weyl manifolds in terms of Killing tensors.

On certain four-dimensional almost Kähler manifolds

100%

Jelonek W.

Colloquium Mathematicum

2007

tom 108

nr 1

7-18

We study four-dimensional almost Kähler manifolds (M,g,J) which admit an opposite almost Kähler structure.

On almost Kähler type (2G₃) 4-manifolds

100%

Jelonek W.

Colloquium Mathematicum

2007

tom 108

nr 1

19-29

We study four-dimensional almost Kähler manifolds (M,g,J) which satisfy A. Gray's condition (G₃).

Homogeneous Riemannian manifolds with generic Ricci tensor

100%

Jelonek W.

2001

tom 77

nr 3

271-287

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.

Toric Hermitian surfaces and almost Kähler structures

100%

Jelonek W.

nr 3

203-217

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.

3-K-contact Wolf spaces

100%

Jelonek W.

2003

tom 82

nr 2

137-148

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.

Holomorphically pseudosymmetric Kähler metrics on ℂℙⁿ

100%

Jelonek W.

Colloquium Mathematicum

2012

tom 127

nr 1

127-131

The aim of this paper is to present examples of holomorphically pseudosymmetric Kähler metrics on the complex projective spaces ℂℙⁿ, where n ≥ 2.

QCH Kähler manifolds with κ = 0

100%

Jelonek W.

Colloquium Mathematicum

2014

tom 136

nr 1

31-40

The aim of this paper is to describe all Kähler manifolds with quasi-constant holomorphic sectional curvature with κ = 0.

Compact holomorphically pseudosymmetric Kähler manifolds

100%

Jelonek W.

Colloquium Mathematicum

2009

tom 117

nr 2

243-249

The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kähler manifolds.

Killing tensors and warped product

100%

Jelonek W.

2000

tom 75

nr 1

15-33

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 $∇_{X} ϱ(X,X) = 2/(n+2) Xτg(X,X)$

Quaternionic-Kähler geometry and almost Kähler A-manifolds

100%

Jelonek W.

2000

tom 75

nr 2

111-124

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.

Einstein-Hermitian and anti-Hermitian 4-manifolds

100%

Jelonek W.

2003

tom 81

nr 1

7-24

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.