Non-existence of almost K�hler structure on hyperbolic spaces of dimension2n(?4)

Oguro, Takashi; Sekigawa, Kouei

doi:10.1007/bf01450489

Cited by 14 publications

(5 citation statements)

References 4 publications

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“…Moreover, combining the results stated in [10] and [13], any connected R 3almost Kähler manifold with p.c.a.s.c. and dim M ≥ 6 turns out to be a complex space-form.…”

supporting

confidence: 59%

Almost Kähler manifolds whose antiholomorphic sectional curvature is pointwise constant

Falcitelli¹,

Farinola²,

Kassabov³

2010

Preprint

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We prove that an almost Kähler manifold (M, g, J) with dim M ≥ 8 and pointwise constant antiholomorphic sectional curvature is a complex spaceform. -Introduction and preliminariesLet (M, g, J) be a 2n-dimensional almost Hermitian manifold. A 2-plane α in the tangent space T x M at a point x of M is antiholomorphic if it is orthogonal to Jα.The manifold (M, g, J) has pointwise constant antiholomorphic sectional curvature (p.c.a.s.c.) ν if, at any point x, the Riemannian sectional curvature ν(x) = K x (α) is independent on the choice of the antiholomorphic 2-plane α in T x M.If (g, J) is a Kähler structure, the previous condition means that (M, g, J) is a complex space-form, i.e. a Kähler manifold with constant holomorphic sectional curvature µ = 4ν ([2]). Moreover, the Riemannian curvature tensor R satisfies:ν being a constant function and π 1 , π 2 the tensor fields such that:

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“…Moreover, combining the results stated in [10] and [13], any connected R 3almost Kähler manifold with p.c.a.s.c. and dim M ≥ 6 turns out to be a complex space-form.…”

supporting

confidence: 59%

Almost Kähler manifolds whose antiholomorphic sectional curvature is pointwise constant

Falcitelli¹,

Farinola²,

Kassabov³

2010

Preprint

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“…According to [7] and [8] a conformal flat AK 3 -manifold of dimension ≥ 4 must be a 4-or a 6-dimensional manifold of constant sectional curvature, or a flat Kähler manifold, or a product of two almost Kähler manifolds M 1 and M 2 of constant sectional curvature c and −c, c > 0, respectively. On the other hand by [10] an almost Kähler manifold of constant sectional curvature and dimension ≥ 4 is a flat Kähler manifold. Hence the assertion follows.…”

Section: The Main Resultmentioning

confidence: 99%

On Bochner flat almost Kahler manifolds

Kassabov

2015

Preprint

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“…It is known that many of these admit orthogonal almost complex structures (iff its Euler characteristic is divisible by four), but cannot admit neither a compatible complex structure [3,10] nor a compatible symplectic structure [17]. We do not know whether these manifolds have a minimizer or not.…”

Section: Hyperbolic 4-manifoldsmentioning

confidence: 98%

Orthogonal almost-complex structures of minimal energy

Bor

Hernández-Lamoneda

Salvai³

2007

Geom Dedicata

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In this article we apply a Bochner type formula to show that on a compact conformally flat riemannian manifold (or half-conformally flat in dimension 4) certain types of orthogonal almost-complex structures, if they exist, give the absolute minimum for the energy functional. We give a few examples when such minimizers exist, and in particular, we prove that the standard almost-complex structure on the round S 6 gives the absolute minimum for the energy. We also discuss the uniqueness of this minimum and the extension of these results to other orthogonal G-structures.

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Non-existence of almost K�hler structure on hyperbolic spaces of dimension2n(?4)

Cited by 14 publications

References 4 publications

Almost Kähler manifolds whose antiholomorphic sectional curvature is pointwise constant

Almost Kähler manifolds whose antiholomorphic sectional curvature is pointwise constant

On Bochner flat almost Kahler manifolds

Orthogonal almost-complex structures of minimal energy

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