Counterexamples to Goldberg Conjecture with Reversed Orientation on Walker 8-Manifolds of Neutral Signature

2017 ◽  
pp. 101-114
Author(s):  
Yasuo Matsushita ◽  
Peter R. Law
Keyword(s):  
Goldberg Conjecture

Para-Kähler–Einstein structures on Walker 4-manifolds

2016 ◽  
Vol 13 (02) ◽  
pp. 1650006
Author(s):  
Murat Iscan ◽  
Gulnur Caglar
Keyword(s):  
Riemannian Manifold ◽  
Goldberg Conjecture ◽  
Walker Manifold

A 4-dimensional Walker manifold [Formula: see text] is a semi-Riemannian manifold [Formula: see text] of signature (++––) (or neutral), which admits a field of null 2-plane. The goal of this paper is to study certain almost paracomplex structures [Formula: see text] on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the para-Kähler forms are symplectic. We show that such a Walker 4-manifold can carry a class of indefinite para-Kähler–Einstein 4-manifolds, examples of indefinite para-Kähler 4-manifolds, and also almost indefinite para-Hermitian–Einstein 4-manifold. Finally, we give a counterexample for the almost para-Hemitian version of Goldberg conjecture.

The four-dimensional goldberg conjecture is true for almost K�hler submersions

2000 ◽  
Vol 69 (1-2) ◽  
pp. 215-226
Author(s):  
Bill Watson
Keyword(s):  
Goldberg Conjecture

A NOTE ON THE GOLDBERG CONJECTURE OF WALKER MANIFOLDS

2011 ◽  
Vol 08 (05) ◽  
pp. 925-928 ◽  
Author(s):  
A. A. SALIMOV
Keyword(s):  
Compact Manifold ◽  
Complex Structure ◽  
Additional Restriction ◽  
Almost Complex Structure ◽  
Almost Complex ◽  
Walker Metric ◽  
Almost Kähler ◽  
Goldberg Conjecture ◽  
Walker Manifold

This paper is concerned with Goldberg conjecture. Using the ϕφ-operator we prove the following result. Let (M, φ, w g) be an almost Kähler–Walker–Einstein compact manifold with the proper almost complex structure φ. The proper almost complex structure φ on Walker manifold (M, w g) is integrable if ϕφgN+ = 0, where gN+ is the induced Norden–Walker metric on M. This resolves a conjecture of Goldberg under the additional restriction on Norden–Walker metric (gN+ ∈ Ker ϕφ).

scholarly journals A remark on four-dimensional almost Kähler-Einstein manifolds with negative scalar curvature

2004 ◽  
Vol 2004 (35) ◽  
pp. 1837-1842 ◽  
Author(s):  
R. S. Lemence ◽  
T. Oguro ◽  
K. Sekigawa
Keyword(s):  
Scalar Curvature ◽  
Einstein Manifolds ◽  
Almost Kähler ◽  
Goldberg Conjecture

Concerning the Goldberg conjecture, we will prove a result obtained by applying the result of Iton in terms ofL2-norm of the scalar curvature.

A Generalization of the Goldberg Conjecture for CoKähler Manifolds

2015 ◽  
Vol 13 (5) ◽  
pp. 2679-2690 ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Goldberg Conjecture

Notes on the Goldberg Conjecture in Dimension Four

2007 ◽  
pp. 221-233 ◽  
Author(s):  
Takashi Oguro ◽  
Kouei Sekigawa
Keyword(s):  
Goldberg Conjecture

scholarly journals The odd-dimensional Goldberg conjecture

2006 ◽  
Vol 279 (9-10) ◽  
pp. 948-952 ◽  
Author(s):  
Vestislav Apostolov ◽  
Tedi Drăghici ◽  
Andrei Moroianu
Keyword(s):  
Goldberg Conjecture
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