scholarly journals Ricci solitons on CR submanifolds of maximal CR dimension in complex projective space

2016 ◽  
Vol 32 (2) ◽  
pp. 189-193
Author(s):  
MIRCEA CRASMAREANU ◽  
◽  
LAURIAN-IOAN PISCORAN ◽  
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Second Order ◽  
Ricci Solitons ◽  
Tensor Fields ◽  
Natural Conditions ◽  
Order Tensor ◽  
Complex Projective ◽  
Cr Submanifolds

We study parallel and symmetric second order tensor fields on CR submanifolds of maximal CR dimension of the complex projective space. Under some natural conditions, these tensors are scalar multiples of the metric; an example of submanifold satisfying these assumptions is the geodesic hypersphere. The result is used for Ricci solitons on these CR submanifolds.

Remarks on Kähler–Ricci solitons

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Lucio Bedulli ◽  
Anna Gori
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Ricci Soliton ◽  
Compact Complex Manifold ◽  
Ricci Solitons ◽  
Complex Projective

AbstractWe prove that a compact complex manifold endowed with a Kähler-Ricci soliton cannot be isometrically embedded in a complex projective space ℂℙ

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