Locally conformal Kähler structures on compact nilmanifolds with left-invariant complex structures

2007 ◽  
Vol 125 (1) ◽  
pp. 93-101 ◽  
Author(s):  
Hiroshi Sawai
Keyword(s):  
Complex Structures ◽  
Locally Conformal Kähler ◽  
Compact Nilmanifolds ◽  
Locally Conformal ◽  
Kähler Structures

scholarly journals Example of a six-dimensional LCK solvmanifold

2017 ◽  
Vol 4 (1) ◽  
pp. 37-42
Author(s):  
Hiroshi Sawai
Keyword(s):  
Lie Group ◽  
Locally Conformal Kähler ◽  
Locally Conformal ◽  
Lee Form ◽  
Solvable Lie Group

Abstract The purpose of this paper is to prove that there exists a lattice on a certain solvable Lie group and construct a six-dimensional locally conformal Kähler solvmanifold with non-parallel Lee form.

scholarly journals A NATURAL CONNECTION ON A BASIC CLASS OF RIEMANNIAN PRODUCT MANIFOLDS

2012 ◽  
Vol 09 (07) ◽  
pp. 1250057 ◽  
Author(s):  
DOBRINKA GRIBACHEVA
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Flat Connection ◽  
Riemannian Product ◽  
Natural Connection ◽  
Hermitian Geometry ◽  
Locally Conformal Kähler ◽  
Basic Class ◽  
Necessary And Sufficient ◽  
Locally Conformal

A Riemannian manifold M with an integrable almost product structure P is called a Riemannian product manifold. Our investigations are on the manifolds (M, P, g) of the largest class of Riemannian product manifolds, which is closed with respect to the group of conformal transformations of the metric g. This class is an analogue of the class of locally conformal Kähler manifolds in almost Hermitian geometry. In the present paper we study a natural connection D on (M, P, g) (i.e. DP = Dg = 0). We find necessary and sufficient conditions, the curvature tensor of D to have properties similar to the Kähler tensor in Hermitian geometry. We pay attention to the case when D has a parallel torsion. We establish that the Weyl tensors for the connection D and the Levi-Civita connection coincide as well as the invariance of the curvature tensor of D with respect to the usual conformal transformation. We consider the case when D is a flat connection. We construct an example of the considered manifold by a Lie group where D is a flat connection with non-parallel torsion.

scholarly journals Examples of non-trivial rank in locally conformal Kähler geometry

2010 ◽  
Vol 270 (1-2) ◽  
pp. 179-187 ◽  
Author(s):  
Maurizio Parton ◽  
Victor Vuletescu
Keyword(s):  
Kahler Geometry ◽  
Locally Conformal Kähler ◽  
Locally Conformal
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