scholarly journals The second-order tangent bundle with deformed 2nd lift metric

2019 ◽  
Vol 16 (04) ◽  
pp. 1950062
Author(s):  
Abdullah Magden ◽  
Kubra Karaca ◽  
Aydin Gezer
Keyword(s):  
Tangent Bundle ◽  
Tensor Field ◽  
Complex Structure ◽  
Sufficient Conditions ◽  
Second Order ◽  
Riemannian Curvature Tensor ◽  
Almost Complex ◽  
Horizontal Part ◽  
Order Tangent ◽  
Second Order Tangent Bundle

Let [Formula: see text] be a pseudo-Riemannian manifold and [Formula: see text] be its second-order tangent bundle equipped with the deformed [Formula: see text]nd lift metric [Formula: see text] which is obtained from the [Formula: see text]nd lift metric by deforming the horizontal part with a symmetric [Formula: see text]-tensor field [Formula: see text]. In the present paper, we first compute the Levi-Civita connection and its Riemannian curvature tensor field of [Formula: see text]. We give necessary and sufficient conditions for [Formula: see text] to be semi-symmetric. Secondly, we show that [Formula: see text] is a plural-holomorphic [Formula: see text]-manifold with the natural integrable nilpotent structure. Finally, we get the conditions under which [Formula: see text] with the [Formula: see text]nd lift of an almost complex structure is an anti-Kähler manifold.

Geometry of second order tangent bundle

2015 ◽  
pp. 245-272
Author(s):  
C. T. J. Dodson ◽  
George Galanis ◽  
Efstathios Vassiliou
Keyword(s):  
Tangent Bundle ◽  
Second Order ◽  
Order Tangent ◽  
Second Order Tangent Bundle

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.

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 Compact Hermitian surfaces of pointwise constant holomorphic sectional curvature

1995 ◽  
Vol 37 (3) ◽  
pp. 343-349 ◽  
Author(s):  
Kouei Sekigawa ◽  
Takashi Koda
Keyword(s):  
Sectional Curvature ◽  
Differentiable Function ◽  
Tangent Bundle ◽  
Complex Structure ◽  
Hermitian Manifold ◽  
Holomorphic Sectional Curvature ◽  
Almost Complex Structure ◽  
Almost Hermitian Manifold ◽  
Almost Complex ◽  
Unit Tangent Bundle

Let M = (M, J, g) be an almost Hermitian manifold and U(M)the unit tangent bundle of M. Then the holomorphic sectional curvature H = H(x) can be regarded as a differentiable function on U(M). If the function H is constant along each fibre, then M is called a space of pointwise constant holomorphic sectional curvature. Especially, if H is constant on the whole U(M), then M is called a space of constant holomorphic sectional curvature. An almost Hermitian manifold with an integrable almost complex structure is called a Hermitian manifold. A real 4-dimensional Hermitian manifold is called a Hermitian surface. Hermitian surfaces of pointwise constant holomorphic sectional curvature have been studied by several authors (cf. [2], [3], [5], [6] and so on).

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.

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