# If there is an irreducible quaternion-Kähler symmetric space of the form G /( Sp ( 1 ) · K ), then H is a non-symmetric irreducible affine holonomy groups, as is C * · H if dim V

In differential geometry, a quaternion-Kähler manifold ( or quaternionic Kähler manifold ) is a Riemannian manifold whose Riemannian holonomy group is a subgroup of Sp ( n )· Sp ( 1 ).

However, these are often excluded from the definition of a quaternion-Kähler manifold by imposing the condition that the scalar curvature is nonzero, or that the holonomy group is equal to Sp ( n )· Sp ( 1 ).

If an Einstein constant of a quaternion-Kähler manifold is zero, it is hyperkähler.

It is conjectured that all quaternion-Kähler manifolds with positive Ricci curvature are symmetric.

The converse is also true: a projective Fano manifold which admits a holomorphic contact structure is always a twistor space, hence quaternion-Kähler geometry with positive Ricci curvature is essentially equivalent to the geometry of holomorphic contact Fano manifolds.

A new South is emerging after the post-bellum years of hesitation, uncertainty, and lack of action from the Negro in defining his new role in the amorphously defined socio-political organizations of the white man.

A small business is defined as one which is independently owned and operated and which is not dominant in its field.

Field shifts were derived from the mean value of the resonance line, defined as the field about which the first moment is zero.

Dirt, which is here defined as particulate material which is usually inorganic and is very often extremely finely divided so as to exhibit colloidal properties.

The international unit is equipotent with the USP unit adopted in 1952, which was defined as the amount of activity present in 20 mg of the USP reference substance.

The function f{t} defined in this way is multi-valued.

In some neighborhood of an isolated tangent point in the f-plane, say Af, the function Af is either double-valued or has no values defined, except at the tangent point itself, where it is single-valued.

Suppose Af is defined in the sub-interval Af.

Where boundary maintenance describes the boundaries or limits of the group, systemic linkage is defined `` as the process whereby one or more of the elements of at least two social systems is articulated in such a manner that the two systems in some ways and on some occasions may be viewed as a single unit.

The positive Kohnstamm reactivity in Condition 1 ( ( the naive state ) is not adequately explained by such a concept as suggestibility ( if suggestibility is defined as the influence on behavior by verbal cues ).

For example, property `` used in the trade or business '' of a transferor corporation, as defined in section 1231, presumably would not retain its special status following a non-taxable reorganization if it is not so used in the business of the acquiring corporation.

Planes defined as parallel to the surface also cut through it into real space, and a depth is suggested optically which is greater than that established pictorially.

**yc is defined by the geometry of the knife ; ;

The gyro angular momentum is defined by H.

But since this is a world in which people disagree about ends and goals and concerning justice and injustice, and since, in a situation where direct action and economic pressure are called for, the justice of the matter has either not been clearly defined by law or the law is not effectively present, there has to be a morality of means applied in every case in which people take it upon themselves to use economic pressures or other forms of force.

Anarchism is generally defined as the political philosophy which holds the state to be undesirable, unnecessary, and harmful ,< ref name =" definition ">

But there's one thing I never seen or heard of, one thing I just don't think there is, and that's a sportin' way o' killin' a man ''!!

I seized the rack and made a western-style flying-mount just in time, one of my knees mercifully landing on my duffel bag -- and merely wrecking my camera, I was to discover later -- my other knee landing on the slivery truck floor boards and -- but this is no medical report.

The true artist is like one of those scientists who, from a single bone can reconstruct an animal's entire body.

In fact, one important aspect of their very religion is the annihilation of men ''.

It took thirty of our women almost six moons to build this one, which is higher and stronger than the old one.

I clapped the big man with the bleached hair on his shoulder and said heartily, hoping it would make an impression on the women: `` This one is the maku Frayne.

`` This one is a tender chicken, oui??

but he presents it publicly so enmeshed in hypocrisy that it is not an honest one.

My definition of this much abused adjective is that a reconstructed rebel is one who is glad that the North won the War.

For one thing, this is not a subject often discussed or analyzed.

The general acceptance of the idea of governmental ( i.e., societal ) responsibility for the economic well-being of the American people is surely one of the two most significant watersheds in American constitutional history.

A third, one of at least equal and perhaps even greater importance, is now being traversed: American immersion and involvement in world affairs.

Today, as new nations rise from the former colonial empires, nationalism is one of the hurricane forces loose in the world.

Historically, however, the concept is one that has been of marked benefit to the people of the Western civilizational group.

It is one of the ironic quirks of history that the viability and usefulness of nationalism and the territorial state are rapidly dissipating at precisely the time that the nation-state attained its highest number ( approximately 100 ).

But it is more than irony: one of the main reasons why nationalism is no longer a tenable concept is because it has spread throughout the planet.

Accidental war is so sensitive a subject that most of the people who could become directly involved in one are told just enough so they can perform their portions of incredibly complex tasks.

Only one rule prevailed in my conversations with these men: The more highly placed they are -- that is, the more they know -- the more concerned they have become.

However, the system is designed, ingeniously and hopefully, so that no one man could initiate a thermonuclear war.