A CANONICAL HYPERKÄHLER METRIC ON THE TOTAL SPACE OF A COTANGENT BUNDLE

2001 ◽  
Author(s):  
D. KALEDIN
Keyword(s):  
Cotangent Bundle ◽  
Total Space

scholarly journals Symmetries of the space of connections on a principal G-bundle and related symplectic structures

2019 ◽  
Vol 31 (10) ◽  
pp. 1950039
Author(s):  
Grzegorz Jakimowicz ◽  
Anatol Odzijewicz ◽  
Aneta Sliżewska
Keyword(s):  
Normal Subgroup ◽  
Cotangent Bundle ◽  
Total Space ◽  
Symplectic Structures ◽  
Structural Group ◽  
Reduction Procedure ◽  
One To One ◽  
Natural Way

There are two groups which act in a natural way on the bundle [Formula: see text] tangent to the total space [Formula: see text] of a principal [Formula: see text]-bundle [Formula: see text]: the group [Formula: see text] of automorphisms of [Formula: see text] covering the identity map of [Formula: see text] and the group [Formula: see text] tangent to the structural group [Formula: see text]. Let [Formula: see text] be the subgroup of those automorphisms which commute with the action of [Formula: see text]. In the paper, we investigate [Formula: see text]-invariant symplectic structures on the cotangent bundle [Formula: see text] which are in a one-to-one correspondence with elements of [Formula: see text]. Since, as it is shown here, the connections on [Formula: see text] are in a one-to-one correspondence with elements of the normal subgroup [Formula: see text] of [Formula: see text], so the symplectic structures related to them are also investigated. The Marsden–Weinstein reduction procedure for these symplectic structures is discussed.

Une caractérisation du fibré cotangent

1988 ◽  
Vol 38 (3) ◽  
pp. 465-472 ◽  
Author(s):  
Tong van Duc
Keyword(s):  
Lie Algebra ◽  
Direct Product ◽  
Cotangent Bundle ◽  
Vector Fields ◽  
Total Space ◽  
Lie Derivation ◽  
Infinitesimal Automorphisms

We prove that the Lie algebra of infinitesimal automorphisms of the cotangent structure on the total space of the cotangent bundle of a manifold is isomorphic to the semi-direct product of the Lie algebra of the vector fields on the manifold by the space of closed 1-forms, the vector fields operating on the forms by Lie derivation. The derivations of this algebra Lie are completely determined and we prove that it characterises the cotangent bundle.

ON MODULI SPACE OF HIGGS Gp(2n, ℂ)-BUNDLES OVER A RIEMANN SURFACE

2010 ◽  
Vol 07 (02) ◽  
pp. 311-322
Author(s):  
INDRANIL BISWAS ◽  
SARBESWAR PAL
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Hilbert Scheme ◽  
Symplectic Form ◽  
Cotangent Bundle ◽  
Symplectic Structure ◽  
Topological Type ◽  
Total Space ◽  
The Other ◽  
Complex Variety

Let X be a compact connected Riemann surface; the holomorphic cotangent bundle of X will be denoted by KX. Let [Formula: see text] denote the moduli space of semistable Higgs Gp (2n, ℂ)-bundles over X of fixed topological type. The complex variety [Formula: see text] has a natural holomorphic symplectic structure. On the other hand, for any ℓ ≥ 1, the Liouville symplectic from on the total space of KX defines a holomorphic symplectic structure on the Hilbert scheme Hilb ℓ(KX) parametrizing the zero-dimensional subschemes of KX. We relate the symplectic form on Hilb ℓ(KX) with the symplectic form on [Formula: see text].

scholarly journals A Study on the Para-Holomorphic Sectional Curvature of Para-Kähler Cotangent Bundles

2015 ◽  
Vol 61 (1) ◽  
pp. 253-262
Author(s):  
S. L. Druţă-Romaniuc
Keyword(s):  
Sectional Curvature ◽  
Cotangent Bundle ◽  
Total Space ◽  
Holomorphic Sectional Curvature ◽  
Kähler Structure ◽  
Nonzero Constant ◽  
Cotangent Bundles

Abstract We obtain the conditions under which the total space T *M of the cotangent bundle, endowed with a natural diagonal para-Kähler structure (G, P), has constant para-holomorphic sectional curvature. Moreover we prove that (T *M,G, P) cannot have nonzero constant para-holomorphic sectional curvature.

scholarly journals Variation formulas for principal functions, II: Applications to variation for harmonic spans

2011 ◽  
Vol 204 ◽  
pp. 19-56 ◽  
Author(s):  
Sachiko Hamano ◽  
Fumio Maitani ◽  
Hiroshi Yamaguchi
Keyword(s):  
Direct Application ◽  
Total Space ◽  
Geometric Meaning ◽  
Principal Function ◽  
Variation Formula ◽  
Circular Slit ◽  
Moving Domain

AbstractA domainD⊂ Czadmits the circular slit mappingP(z) fora, b∈Dsuch thatP(z) – 1/(z–a) is regular ataandP(b) = 0. We callp(z) =log|P(z)|theLi-principal functionandα= log |P′(b)| theL1-constant, and similarly, the radial slit mappingQ(z) implies theL0-principal functionq(z) and theL0-constantβ. We calls=α–βtheharmonic spanfor (D, a, b). We show the geometric meaning ofs. Hamano showed the variation formula for theL1-constantα(t) for the moving domainD(t) in Czwitht∈B:= {t∈ C: |t| <ρ}. We show the corresponding formula for theL0-constantβ(t) forD(t) and combine these to prove that, if the total spaceD =∪t∈B(t, D(t)) is pseudoconvex inB× Cz, thens(t) is subharmonic onB. As a direct application, we have the subharmonicity of log coshd(t) onB, whered(t) is the Poincaré distance betweenaandbonD(t).

scholarly journals SCATTERING, GREEN’S FUNCTIONS AND SYMMETRIES IN A TOTAL SPACE OF A DIRAC MONOPOLE FIBRE BUNDLE

1991 ◽  
Vol 06 (04) ◽  
pp. 577-598 ◽  
Author(s):  
A.G. SAVINKOV ◽  
A.B. RYZHOV
Keyword(s):  
Green's Functions ◽  
Principal Bundle ◽  
Fibre Bundle ◽  
Green’S Functions ◽  
Wave Functions ◽  
Total Space ◽  
Dirac Monopole ◽  
Hidden Symmetries ◽  
Scattering Wave ◽  
A Charge

The scattering wave functions and Green’s functions were found in a total space of a Dirac monopole principal bundle. Also, hidden symmetries of a charge-Dirac monopole system and those joining the states relating to different topological charges n=2eg were found.

scholarly journals Horizontal lifts from a manifold to its cotangent bundle

1967 ◽  
Vol 19 (2) ◽  
pp. 185-198 ◽  
Author(s):  
K. YANO ◽  
E. M. PATTERSON
Keyword(s):  
Cotangent Bundle

scholarly journals Affine varieties, singularities and the growth rate of wrapped Floer cohomology

2018 ◽  
Vol 10 (03) ◽  
pp. 493-530
Author(s):  
Mark McLean
Keyword(s):  
Growth Rate ◽  
Cotangent Bundle ◽  
Betti Numbers ◽  
Symplectic Manifolds ◽  
Isolated Singularity ◽  
Contact Manifolds ◽  
Floer Cohomology ◽  
Complex Singularities ◽  
Smooth Affine ◽  
Simply Connected

In this paper, we give partial answers to the following questions: Which contact manifolds are contactomorphic to links of isolated complex singularities? Which symplectic manifolds are symplectomorphic to smooth affine varieties? The invariant that we will use to distinguish such manifolds is called the growth rate of wrapped Floer cohomology. Using this invariant we show that if [Formula: see text] is a simply connected manifold whose unit cotangent bundle is contactomorphic to the link of an isolated singularity or whose cotangent bundle is symplectomorphic to a smooth affine variety then M must be rationally elliptic and so it must have certain bounds on its Betti numbers.

scholarly journals SOME NOTES ON THE MODIFIED RIEMANNIAN EXTENSION g ̃_(∇,c) ON COTANGENT BUNDLE

2020 ◽  
Vol 20 (4) ◽  
pp. 931-940
Author(s):  
HASIM CAYIR
Keyword(s):  
Cotangent Bundle ◽  
Vector Fields ◽  
Lie Derivatives ◽  
Complete And Vertical Lifts

In this paper, we define the modified Riemannian extension g ̃_(∇,c) in the cotangent bundle T^* M, which is completely determined by its action on complete lifts of vector fields. Later, we obtain the covarient and Lie derivatives applied to the modified Riemannian extension with respect to the complete and vertical lifts of vector and kovector fields, respectively.

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