scholarly journals A new class of almost complex structures on tangent bundle of a Riemannian manifold

2018 ◽  
Vol 26 (2) ◽  
pp. 137-145
Author(s):  
Amir Baghban ◽  
Esmaeil Abedi
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Integrability Condition ◽  
Complex Structure ◽  
Riemannian Metric ◽  
Curvature Operator ◽  
Complex Structures ◽  
New Class ◽  
Almost Complex Structures ◽  
Almost Complex

AbstractIn this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

scholarly journals BRANCHED SHADOWS AND COMPLEX STRUCTURES ON 4-MANIFOLDS

2008 ◽  
Vol 17 (11) ◽  
pp. 1429-1454 ◽  
Author(s):  
FRANCESCO COSTANTINO
Keyword(s):  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Homotopy Classes ◽  
Almost Complex Structures ◽  
Almost Complex

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spinc-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-dimensional handlebody is homotopic to a complex one.

A new class of almost complex structures

1995 ◽  
Vol 168 (1) ◽  
pp. 133-149
Author(s):  
Chuan -Chih Hsiung ◽  
Bonnie Xiong
Keyword(s):  
Complex Structures ◽  
New Class ◽  
Almost Complex Structures ◽  
Almost Complex

On the Relation of Real and Complex Lie Supergroups

2015 ◽  
Vol 58 (2) ◽  
pp. 281-284 ◽  
Author(s):  
Matthias Kalus
Keyword(s):  
Complex Structure ◽  
Sufficient Conditions ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
New Approach ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Lie Supergroups ◽  
Necessary And Sufficient

AbstractA complex Lie supergroup can be described as a real Lie supergroup with integrable almost complex structure. The necessary and sufficient conditions on an almost complex structure on a real Lie supergroup for defining a complex Lie supergroup are deduced. The classification of real Lie supergroups with such almost complex structures yields a new approach to the known classification of complex Lie supergroups by complexHarish-Chandra superpairs. A universal complexi ûcation of a real Lie supergroup is constructed

scholarly journals On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures

2021 ◽  
pp. 2150075
Author(s):  
Andrea Cattaneo ◽  
Antonella Nannicini ◽  
Adriano Tomassini
Keyword(s):  
Complex Structure ◽  
Kodaira Dimension ◽  
Classification Theory ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Almost Complex Manifolds ◽  
Kähler Structure ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Almost Kähler

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact [Formula: see text]-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text]. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover, we prove Ricci flatness of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally, we construct a natural hypercomplex structure providing a twistorial description.

scholarly journals Weakly complex homogeneous spaces

2014 ◽  
Vol 2014 (691) ◽  
Author(s):  
Andrei Moroianu ◽  
Uwe Semmelmann
Keyword(s):  
Tangent Bundle ◽  
Symmetric Spaces ◽  
Homogeneous Spaces ◽  
Complex Structure ◽  
Complex Spaces ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Complex Tangent ◽  
Recent Classification ◽  
Simply Connected

Abstract.We complete our recent classification (2011) of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank homogeneous space has weakly complex tangent bundle if and only if it is a product of compact equal rank homogeneous spaces which either carry an invariant almost complex structure (and are classified by Hermann (1955)), or have stably trivial tangent bundle (and are classified by Singhof and Wemmer (1986)), or belong to an explicit list of weakly complex spaces which have neither stably trivial tangent bundle, nor carry invariant almost complex structures.

Remarks about the Kaluza-Klein metric on tangent bundle

2019 ◽  
Vol 16 (03) ◽  
pp. 1950040
Author(s):  
Murat Altunbas ◽  
Lokman Bilen ◽  
Aydin Gezer
Keyword(s):  
Tangent Bundle ◽  
Complex Structure ◽  
Sufficient Conditions ◽  
Complex Structures ◽  
Almost Complex ◽  
Compatible Almost Complex Structure ◽  
Almost Kähler ◽  
Necessary And Sufficient ◽  
Curvature Tensors ◽  
Kaluza Klein

The paper is concerned with the Kaluza–Klein metric on the tangent bundle over a Riemannian manifold. All kinds of Riemann curvature tensors are computed and some curvature properties are given. The compatible almost complex structure is defined on the tangent bundle, and necessary and sufficient conditions for such a structure to be integrable are described. Then, the condition is given under which the tangent bundle with these structures is almost Kähler. Finally, almost golden complex structures are defined on this setting and some results related to them are presented.

Harmonicity of proper almost complex structures on Walker 4-manifolds

2017 ◽  
Vol 14 (06) ◽  
pp. 1750094
Author(s):  
Johann Davidov ◽  
Absar Ul-Haq ◽  
Oleg Mushkarov
Keyword(s):  
Twistor Space ◽  
Harmonic Map ◽  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Harmonic Section

Every Walker [Formula: see text]-manifold [Formula: see text], endowed with a canonical neutral metric [Formula: see text], admits a specific almost complex structure called proper. In this paper, we find the conditions under which a proper almost complex structure is a harmonic section or a harmonic map from [Formula: see text] to its hyperbolic twistor space.

scholarly journals S.-S. Chern’s study of almost-complex structures on the six-sphere

2021 ◽  
pp. 2140006
Author(s):  
Robert L. Bryant
Keyword(s):  
Open Problem ◽  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Exceptional Group ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Interesting Class

In April 2003, Chern began a study of almost-complex structures on the six-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group [Formula: see text]. While he did not solve the (currently still open) problem of determining whether there exists an integrable almost-complex structure on [Formula: see text], he did prove a significant identity that resolves the question for an interesting class of almost-complex structures on [Formula: see text].

scholarly journals Symmetries of almost complex structures and pseudoholomorphic foliations

2014 ◽  
Vol 25 (08) ◽  
pp. 1450079 ◽  
Author(s):  
Boris Kruglikov
Keyword(s):  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Integrable Structure ◽  
Infinite Dimensional ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Finite Dimensionality ◽  
Local Symmetries ◽  
Symmetric Structures

Contrary to complex structures, a generic almost complex structure J has no local symmetries. We give a criterion for finite-dimensionality of the pseudogroup G of local symmetries for a given almost complex structure J. It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some integrable structure, like a pseudoholomorphic foliation. We classify the sub-maximal (from the viewpoint of the size of G) symmetric structures J. Almost complex structures in dimensions 4 and 6 are discussed in greater details in this paper.

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