Hermitian Geometry

1985 ◽  
pp. 92-114
Author(s):  
Wilhelm Stoll
Keyword(s):  
Hermitian Geometry

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 Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds

2018 ◽  
Vol 67 (3) ◽  
pp. 1800093 ◽  
Author(s):  
Vincenzo E. Marotta ◽  
Richard J. Szabo
Keyword(s):  
Hermitian Geometry

Hermitian geometry and involutive algebras

1985 ◽  
Vol 188 (3) ◽  
pp. 359-382 ◽  
Author(s):  
Mircea Martin
Keyword(s):  
Hermitian Geometry

scholarly journals Balanced Hermitian geometry on 6-dimensional nilmanifolds

2015 ◽  
Vol 27 (2) ◽  
Author(s):  
Luis Ugarte ◽  
Raquel Villacampa
Keyword(s):  
Proper Subgroup ◽  
Complex Structure ◽  
Holonomy Group ◽  
Hermitian Geometry

AbstractThe invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the (restricted) holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if

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