The set of all isometric operators which can be extended to be a linear

isometry of X into Y is denoted by [J.sub.l].

The condition factor increases from November to February, while the

isometry factor decreases, during the months of maximum maturation stage.

It is important to note that because the major axis is not coincident with

isometry it summarizes some shape variation (and as well, the remaining axes explain some size variation).

Then we define coordinate charts [Mathematical Expression Omitted] as the composition of the linear

isometry of Euclidean space to the tangent space at [Mathematical Expression Omitted] taking the standard frame to the frame [Mathematical Expression Omitted] with the exponential map at [Mathematical Expression Omitted] into [M.sub.k].

If there is no global

isometry carrying g on to g!prime^, then the 'past' does not determine the 'future' even up to isomorphism.

Let A = DU be the polar decomposition of A, where U is an

isometry and D = [square root of (A*A)] is non-negative.

Non avian theropods and ungulates showed a negative allometry, feline's

isometry and birds a positive allometry in the lower leg (Table I).

Consequently, once an initial condition has been chosen, there exists a unique

isometry [bar.h] [member of] Isom([N.sub.o], [[bar.g].sub.o]) preserving the Killing fiber flow ([[bar.h].sub.*[xi] = [xi]) and satisfying [[pi].sub.o] [??] [bar.h] = h [??] [[pi].sub.o].

In this paper an

isometry means a complex-linear

isometry.

Currently, Gregory is the chairman and CEO of

Isometry Advisors Inc as well as a director at Iconic Therapeutics and the Sosei Group Corporation.

Then M has the holonomy representation: [Hol.sub.M] : [[pi].sub.1](M, *) [right arrow] [Isom.sup.+][H.sup.3], where [Isom.sup.+][H.sup.3] is the orientation preserving

isometry group of hyperbolic 3-space [H.sup.3].

In 1964, Forelli [11] showed that every

isometry on [H.sup.p] for 1 < p < [infinity] and p [not equal to] 2 is a weighted composition operator.