The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Róbert Szőke - One of the best experts on this subject based on the ideXlab platform.
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The Tangent Bundle of an Almost Complex Manifold
Canadian Mathematical Bulletin, 2001Co-Authors: László Lempert, Róbert SzőkeAbstract:AbstractMotivated by deformation theory of holomorphic maps between almost Complex Manifolds we endow, in a natural way, the tangent bundle of an almost ComplexManifold with an almost Complex structure. We describe various properties of this structure.
Lars Schafer - One of the best experts on this subject based on the ideXlab platform.
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para tt bundles on the tangent bundle of an almost para Complex Manifold
Annals of Global Analysis and Geometry, 2007Co-Authors: Lars SchaferAbstract:In this paper we study para-tt *-bundles (TM, D, S) on the tangent bundle of an almost para-Complex Manifold (M, τ). We characterise those para-tt *-bundles with \({\nabla=D + S}\) induced by the one-parameter family of connections given by \({\nabla^{\theta}=\exp(\theta \tau) \circ \nabla \circ\exp(-\theta \tau)}\) and prove a uniqueness result for solutions with a para-Complex connection D. Flat nearly para-Kahler Manifolds and special para-Complex Manifolds are shown to be such solutions. We analyse which of these solutions admit metric or symplectic para-tt *-bundles. Moreover, we give a generalisation of the notion of a para-pluriharmonic map to maps from almost para-Complex Manifolds (M, τ) into pseudo-Riemannian Manifolds and associate to the above metric and symplectic para-tt *-bundles generalised para-pluriharmonic maps into \({{{\rm Sp}(\mathbb{R}^{2n})/U^{\pi}(C^n)}}\) , respectively, into SO 0(n,n)/U π(C n ), where U π(C n ) is the para-Complex analogue of the unitary group.
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tt geometry on the tangent bundle of an almost Complex Manifold
Journal of Geometry and Physics, 2007Co-Authors: Lars SchaferAbstract:Abstract The subject of this paper is t t ∗ -bundles ( T M , D , S ) over an almost Complex Manifold ( M , J ) . Let ∇ be a flat connection on M . We characterize those t t ∗ -bundles with ∇ = D + S which are induced by the one parameter family of connections ∇ θ = exp ( θ J ) ∘ ∇ ∘ exp ( − θ J ) and obtain a uniqueness result for solutions where D is Complex. A subclass of such solutions is flat nearly Kahler Manifolds and special Kahler Manifolds. Moreover, we study the case where these t t ∗ -bundles admit the structure of symplectic or metric t t ∗ -bundles. Finally, we generalize the notion of pluriharmonic maps to maps from almost Complex Manifolds ( M , J ) into pseudo-Riemannian Manifolds and relate the above symplectic and metric t t ∗ -bundles to pluriharmonic maps from ( M , J ) into the pseudo-Riemannian symmetric spaces S O 0 ( p , q ) / U ( p , q ) and Sp ( R 2 n ) / U ( p , q ) , respectively.
László Lempert - One of the best experts on this subject based on the ideXlab platform.
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The Tangent Bundle of an Almost Complex Manifold
Canadian Mathematical Bulletin, 2001Co-Authors: László Lempert, Róbert SzőkeAbstract:AbstractMotivated by deformation theory of holomorphic maps between almost Complex Manifolds we endow, in a natural way, the tangent bundle of an almost ComplexManifold with an almost Complex structure. We describe various properties of this structure.
Lars Schaefer - One of the best experts on this subject based on the ideXlab platform.
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Para-tt*-bundles on the tangent bundle of an almost para-Complex Manifold
2007Co-Authors: Lars SchaeferAbstract:In this paper we study para-tt*-bundles (TM,D,S) on the tangent bundle of an almost para-Complex Manifold $(M,\tau).$ We characterise those para-tt*-bundles with $\nabla=D+S$ induced by the one-parameter family of connections given by $\nabla^{\theta}=\exp(\theta \tau) \circ \nabla \circ\exp(-\theta \tau)$ and prove a uniqueness result for solutions with a para-Complex connection D. Flat nearly para-Kähler Manifolds and special para-Complex Manifolds are shown to be such solutions. We analyse which of these solutions admit metric or symplectic para-tt*-bundles. Moreover, we give a generalisation of the notion of a para-pluriharmonic map to maps from almost para-Complex Manifolds $(M,\tau)$ into pseudo-Riemannian Manifolds and associate to the above metric and symplectic para-tt*-bundles generalised para-pluriharmonic maps into $\mathrm{Sp}(\bR^{2n})/U^{\pi}(C^n),$ respectively into $ SO_0(n,n)/U^{\pi}(C^n),$ where $U^{\pi}(C^n)$ is the para-Complex analogue of the unitary group.
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tt*-geometry on the tangent bundle of an almost Complex Manifold
Journal of Geometry and Physics, 2007Co-Authors: Lars SchaeferAbstract:The subject of this paper are tt*-bundles (TM,D,S) over an almost Complex Manifold (M,J). Let $\nabla$ be a flat connection on M. We characterize those tt*-bundles with $\nabla=D+S$ which are induced by the one parameter family of connections $\nabla^{\theta} = \exp{(\theta J)} \circ \nabla \circ \exp{(-\theta J)}$ and obtain a uniqueness result for solutions where $D$ is Complex. A subclass of such solutions are flat nearly Kähler Manifolds and special Kähler Manifolds. Moreover, we study the case where these tt*-bundles admit the structure of symplectic or metric tt*-bundles. Finally, we generalize the notion of pluriharmonic maps to maps from almost Complex Manifolds (M,J) into pseudo-Riemannian Manifolds and relate the above symplectic and metric tt*-bundles to pluriharmonic maps from (M,J) into the pseudo-Riemannian symmetric spaces $SO_0(p,q)/U(p,q)$ and $\mathrm{Sp}(\bR^{2n})/U(p,q),$ respectively.
Boris Kruglikov - One of the best experts on this subject based on the ideXlab platform.
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Characteristic distributions on 4-dimensional almost Complex Manifolds
Geometry and Topology of Caustics – Caustics '02, 2003Co-Authors: Boris KruglikovAbstract:In this paper the Nijenhuis tensor characteristic distributions on a non-integrable four-dimensional almost Complex Manifold is investigated for integrability, singularities and equivalence.
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existence of close pseudoholomorphic disks for almost Complex Manifolds and an applications to kobayashi royden pseudonorm
arXiv: Complex Variables, 2000Co-Authors: Boris KruglikovAbstract:In this paper we extend the notion of the Kobayashi-Royden pseudonorm for almost Complex Manifolds. Its basic properties known from the Complex analysis are preserved in the nonintegrable case as well. The main theorem on coincidence of the pseudodistance induced by this pseudonorm with the Kobayashi pseudodistance for the almost Complex Manifold is equivalent to the possibility of deforming slightly a pseudoholomorphic disk in an almost Complex Manifold. We also describe the result in terms of h-principle and consider a geometric application for moduli spaces of pseudoholomorphic curves.
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Pseudoholomorphic mappings and Kobayashi hyperbolicity
Differential Geometry and Its Applications, 1999Co-Authors: Boris Kruglikov, Marius OverholtAbstract:Abstract We extend the definition of the Kobayashi pseudodistance to almost Complex Manifolds and show that its familiar properties are for the most part preserved. We also study the automorphism group of an almost Complex Manifold. We give special consideration to almost Complex structures tamed by some symplectic form. The notions and pseudoholomorphic curves involved are illustrated in some examples.
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The Kobayashi pseudodistance on almost Complex Manifolds
arXiv: Differential Geometry, 1997Co-Authors: Boris Kruglikov, Marius OverholtAbstract:We extend the definition of the Kobayashi pseudodistance to almost Complex Manifolds and show that its familliar properties are for the most part preserved. We also study the automorphism group of an almost Complex Manifold and finish with some examples.
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The Kobayashi pseudodistance on almost Complex Manifolds
1997Co-Authors: Boris Kruglikov, Marius OverholtAbstract:We extend the definition of the Kobayashi pseudodistance to almost Complex Manifolds and show that its familiar properties are for the most part preserved. We also study the automorphism group of an almost Complex Manifold and finish with some examples. The Kobayashi pseudodistance on almost Complex Manifolds Boris S. Kruglikov and Marius Overholt