scholarly journals Complex Connections on Conformal Kähler Manifolds with Norden Metric

2011 ◽  
Author(s):  
Marta Teofilova
Keyword(s):  
Norden Metric

Lie Groups as Four-dimensional Complex Manifolds with Norden Metric

2008 ◽  
Vol 89 (1-2) ◽  
pp. 34-47
Author(s):  
Kostadin Gribachev ◽  
Marta Teofilova
Keyword(s):  
Lie Groups ◽  
Complex Manifolds ◽  
Norden Metric

scholarly journals A note on para-holomorphic Riemannian–Einstein manifolds

2016 ◽  
Vol 13 (09) ◽  
pp. 1650107
Author(s):  
Cristian Ida ◽  
Alexandru Ionescu ◽  
Adelina Manea
Keyword(s):  
Complex Manifold ◽  
Lie Group ◽  
Riemannian Manifolds ◽  
Complex Geometry ◽  
Riemannian Metrics ◽  
Riemannian Metric ◽  
Einstein Metric ◽  
Einstein Manifolds ◽  
Norden Metric ◽  
Norden Metrics

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.

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