norden metric
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2016 ◽  
Vol 13 (09) ◽  
pp. 1650107
Author(s):  
Cristian Ida ◽  
Alexandru Ionescu ◽  
Adelina Manea

The aim of this note is the study of Einstein condition for para-holomorphic Riemannian metrics in the para-complex geometry framework. First, we make some general considerations about para-complex Riemannian manifolds (not necessarily para-holomorphic). Next, using a one-to-one correspondence between para-holomorphic Riemannian metrics and para-Kähler–Norden metrics, we study the Einstein condition for a para-holomorphic Riemannian metric and the associated real para-Kähler–Norden metric on a para-complex manifold. Finally, it is shown that every semi-simple para-complex Lie group inherits a natural para-Kählerian–Norden Einstein metric.



Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 411-425 ◽  
Author(s):  
Mancho Manev

We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric, respectively. They can be combined as the so-called almost contact complex Riemannian manifold. This paper is a survey with additions of results on differential geometry of canonical-type connections (i.e. metric connections with torsion satisfying a certain algebraic identity) on the considered manifolds.



2013 ◽  
Vol 10 (07) ◽  
pp. 1320010 ◽  
Author(s):  
A. A. SALIMOV ◽  
RABIA CAKAN
Keyword(s):  

The main purpose of this paper is to study some properties of bicomplex-holomorphic 4-manifolds endowed with a holomorphic double Walker–Norden metric.







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