scholarly journals Generalized Goldberg Formula

2016 ◽  
Vol 59 (3) ◽  
pp. 508-520
Author(s):  
Antonio De Nicola ◽  
Ivan Yudin
Keyword(s):  
Riemannian Manifold ◽  
Compact Manifold ◽  
Differential Forms ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Sasakian Manifolds ◽  
De Rham ◽  
Locally Conformally Kähler

AbstractIn this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed p-form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel I. Goldberg for the case of 1-forms. As first examples of application we obtain new identities on locally conformally Kähler manifolds and quasi-Sasakian manifolds. Moreover, we prove that under suitable conditions a certain subalgebra of differential forms in a compact manifold is quasi-isomorphic as a CDGA to the full de Rham algebra.

scholarly journals Holomorphic submersions of locally conformally Kähler manifolds

2013 ◽  
Vol 193 (5) ◽  
pp. 1345-1351 ◽  
Author(s):  
Liviu Ornea ◽  
Maurizio Parton ◽  
Victor Vuletescu
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Locally Conformally Kähler

Introduction to Kähler Manifolds

2017 ◽  
Author(s):  
Eduardo Cattani ◽  
Phillip Griffiths
Keyword(s):  
Summer School ◽  
Differential Forms ◽  
Kähler Manifolds ◽  
Theoretical Physics ◽  
Kahler Manifolds ◽  
Complex Manifolds ◽  
Linear Transformations ◽  
Harmonic Forms ◽  
Hodge Structures ◽  
Kähler Structures

This chapter provides an introduction to the basic results on the topology of compact Kähler manifolds that underlie and motivate Hodge theory. This chapter consists of five sections which correspond, roughly, to the five lectures in the course given during the Summer School at the International Centre for Theoretical Physics (ICTP). The five topics under discussion are: complex manifolds; differential forms on complex manifolds; symplectic, Hermitian, and Kähler structures; harmonic forms; and the cohomology of compact Kähler manifolds. There are also two appendices. The first collects some results on the linear algebra of complex vector spaces, Hodge structures, nilpotent linear transformations, and representations of sl(2,ℂ) and serves as an introduction to many other chapters in this volume. The second contains a new proof of the Kähler identities by reduction to the symplectic case.

scholarly journals On toric locally conformally Kähler manifolds

2017 ◽  
Vol 51 (4) ◽  
pp. 401-417 ◽  
Author(s):  
Farid Madani ◽  
Andrei Moroianu ◽  
Mihaela Pilca
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Locally Conformally Kähler
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