scholarly journals Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures

2017 ◽  
Vol 155 (3-4) ◽  
pp. 389-417 ◽  
Author(s):  
A. Andrada ◽  
M. Origlia
Keyword(s):  
Lie Groups ◽  
Symplectic Structures ◽  
Locally Conformal Kähler ◽  
Locally Conformal

scholarly journals Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds

2019 ◽  
Vol 31 (3) ◽  
pp. 563-578
Author(s):  
Marcos Origlia
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Type I ◽  
Symplectic Structures ◽  
Locally Conformal

Abstract We study Lie algebras of type I, that is, a Lie algebra {\mathfrak{g}} where all the eigenvalues of the operator {\operatorname{ad}_{X}} are imaginary for all {X\in\mathfrak{g}} . We prove that the Morse–Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure.

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 Special Types of Locally Conformal Closed G2-Structures

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 90 ◽  
Author(s):  
Giovanni Bazzoni ◽  
Alberto Raffero
Keyword(s):  
Lie Groups ◽  
Symplectic Geometry ◽  
Complete Characterization ◽  
Compact Manifolds ◽  
Different Types ◽  
Simply Connected ◽  
Locally Conformal

Motivated by known results in locally conformal symplectic geometry, we study different classes of G 2 -structures defined by a locally conformal closed 3-form. In particular, we provide a complete characterization of invariant exact locally conformal closed G 2 -structures on simply connected Lie groups, and we present examples of compact manifolds with different types of locally conformal closed G 2 -structures.

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

scholarly journals On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures

1995 ◽  
Vol 18 (2) ◽  
pp. 331-340
Author(s):  
M. Hasan shahid ◽  
A. Sharfuddin
Keyword(s):  
Necessary Conditions ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Kahler Manifold ◽  
Generic Submanifolds ◽  
Locally Conformal Kähler ◽  
Generic Submanifold ◽  
Locally Conformal ◽  
Totally Real

The study ofCR-submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared onCR-submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds andCR-submanifolds of Kähler manifolds. On the other hand, many examplesC2of generic surfaces in which are notCR-submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler manifold with four canonical strucrures, denoted byP,F,tandf, to have parallelP,Fandt. We also prove that for a generic submanifold of a locally conformal Kähler manifold,Fis parallel ifftis parallel.

Sign in / Sign up

Export Citation Format

Share Document