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Every hyperkähler manifold M has a 2-sphere of complex structures ( i. e. integrable almost complex structures ) with respect to which the metric is Kähler.

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## Some Related Sentences

Every and hyperkähler

**(**

__Every__Calabi – Yau

**manifold**in 4

**(**real

**)**dimensions

**is**

**a**

__hyperkähler__

**manifold**, because SU

**(**2

**)**

**is**isomorphic

**to**Sp

**(**1 ).

Every and manifold

*

__Every__Lie group**is**parallelizable, and hence an orientable__manifold__**(**there**is****a**bundle isomorphism between its tangent bundle and**the**product**of**itself**with****the**tangent space at**the**identity**)**__Every__smooth

__manifold__defined in this way

**has**

**a**natural diffeology, for

**which**

**the**plots correspond

**to**

**the**smooth maps from open subsets

**of**R < sup > n </ sup >

**to**

**the**

__manifold__

**.**

__Every__Riemann surface

**is**

**a**two-dimensional real analytic

__manifold__

**(**

**i**

**.**

**e**.,

**a**surface ), but it contains more structure

**(**specifically

**a**

**complex**structure

**)**

**which**

**is**needed for

**the**unambiguous definition

**of**holomorphic functions

**.**

__Every__smooth function G over

**the**symplectic

__manifold__generates

**a**one-parameter family

**of**symplectomorphisms and if

*

__Every__bundle**of**Lie algebras over**a**smooth__manifold__defines**a**Lie algebroid where**the**Lie bracket**is**defined pointwise and**the**anchor map**is**equal**to**zero**.**__Every__Hermitian

__manifold__

**is**

**a**

**complex**

__manifold__

**which**comes naturally equipped

**with**

**a**Hermitian form and an

**integrable**,

**almost**

**complex**structure

**.**

* The embedding theorem for Stein manifolds states

**the**following:__Every__Stein__manifold__**of****complex**dimension can be embedded into by**a**biholomorphic proper map**.**
*

__Every__Stein__manifold__**is**holomorphically spreadable,**i****.****e****.**for every point, there are holomorphic functions defined on all**of****which**form**a**local coordinate system when restricted**to**some open neighborhood**of****.**__Every__compact smooth

__manifold__

**of**dimension 2n,

**which**

**has**only handles

**of**index ≤ n,

**has**

**a**Stein structure provided n > 2, and when n = 2

**the**same holds provided

**the**2-handles are attached

**with**certain framings

**(**framing less than

**the**Thurston-Bennequin framing ).

__Every__complete, connected, simply-connected

__manifold__

**of**constant negative curvature − 1

**is**isometric

**to**

**the**real hyperbolic space H < sup > n </ sup >.

__Every__

__manifold__

**has**an underlying topological

__manifold__, obtained simply by forgetting

**the**additional structure

**.**

Every and M

* In any ring R,

**a**maximal ideal**is**an ideal__M__that**is**maximal in**the**set**of**all proper ideals**of**R,**i****.****e****.**__M__**is**contained in exactly 2 ideals**of**R, namely__M__itself and**the**entire ring R**.**__Every__maximal ideal**is**in fact prime**.**__Every__smooth

**(**or differentiable

**)**map φ:

__M__→ N between smooth

**(**or differentiable

**)**manifolds induces natural linear maps between

**the**corresponding tangent spaces:

__Every__measurable cardinal κ

**is**

**a**0-huge cardinal because < sup > κ </ sup >

__M__⊂

__M__, that

**is**, every function from κ

**to**

__M__

**is**in

__M__

**.**Consequently, V < sub > κ + 1 </ sub >⊂

__M__

**.**

:

__Every__countable theory**which****is**satisfiable in**a**model__M__,**is**satisfiable in**a**countable substructure**of**__M__**.**
* Siegal,

__M__., Cornell Feline Health Center**(**Editors**)****(**1989**)**The Cornell Book**of**Cats: A Comprehensive Medical Reference for__Every__Cat and Kitten**.**__Every__year about 5000 applications are received, out

**of**

**which**about 300 students

**(**around 150 in each year

**)**are enrolled in

**the**2 year full time

__M__

**.**Tech

**.**

__Every__finite-length module

__M__

**has**

**a**composition series, and

**the**length

**of**every such composition series

**is**equal

**to**

**the**length

**of**

__M__

**.**

*

__Every__direct summand**of**__M__**is**pure in__M__**.**Consequently, every subspace**of****a**vector space over**a**field**is**pure**.**

Every and has

__Every__woman

__has__had

**the**experience

**of**saying no when she meant yes, and saying yes when she meant no

**.**

__Every__detail in his interpretation

__has__been beautifully thought out, and

**of**these I would especially cite

**the**delicious laendler touch

**the**pianist brings

**to**

**the**fifth variation

**(**an obvious indication that he

**is**playing

**with**Viennese musicians

**)**, and

**the**gossamer shading throughout

**.**

__Every__family

**of**Riviera Presbyterian Church

__has__been asked

**to**read

**the**Bible and pray together daily during National Christian Family Week and

**to**undertake one project in

**which**all members

**of**

**the**family participate

**.**

__Every__community, if it

**is**alive

__has__

**a**spirit, and that spirit

**is**

**the**center

**of**its unity and identity

**.**

__Every__such subset

__has__

**a**smallest element, so

**to**specify our choice function we can simply say that it maps each set

**to**

**the**least element

**of**that set

**.**

** Zorn's lemma:

__Every__non-empty partially ordered set in**which**every chain**(****i****.****e****.**totally ordered subset**)**__has__an upper bound contains at least one maximal element**.**
The restricted principle "

__Every__partially ordered set__has__**a**maximal totally ordered subset "**is**also equivalent**to**AC over ZF**.**
** Tukey's lemma:

__Every__non-empty collection**of**finite character__has__**a**maximal element**with****respect****to**inclusion**.**
*

__Every__continuous functor on**a**small-complete category**which**satisfies**the**appropriate solution set condition__has__**a**left-adjoint**(****the**Freyd adjoint functor theorem ).__Every__unit

**of**length

__has__

**a**corresponding unit

**of**area, namely

**the**area

**of**

**a**square

**with**

**the**given side length

**.**

__Every__field

__has__an algebraic extension

**which**

**is**algebraically closed

**(**called its algebraic closure ), but proving this in general requires some form

**of**

**the**axiom

**of**choice

**.**

__Every__ATM cell

__has__an 8-or 12-bit Virtual Path Identifier

**(**VPI

**)**and 16-bit Virtual Channel Identifier

**(**VCI

**)**pair defined in its header

**.**

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