Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Many and varied; of many kinds; multiple: our manifold failings.
 adj. Having many features or forms: manifold intelligence.
 adj. Being such for a variety of reasons: a manifold traitor.
 adj. Consisting of or operating several devices of one kind at the same time.
 n. A whole composed of diverse elements.
 n. One of several copies.
 n. A pipe or chamber having multiple apertures for making connections.
 n. Mathematics A topological space or surface.
 transitive v. To make several copies of, as with carbon paper.
 transitive v. To make manifold; multiply.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A copy made by the manifold writing process.
 n. A pipe fitting or similar device that connects multiple inputs or outputs.
 n. The third stomach of a ruminant animal, an omasum.
 n. A topological space that looks locally like the "ordinary" Euclidean space and is Hausdorff.
 adj. Various in kind or quality; many in number; numerous; multiplied; complicated; diverse.
 adj. Exhibited at diverse times or in various ways.
 adv. Many times; repeatedly.
 v. To make manifold; multiply.
 v. To multiply or reproduce impressions of by a single operation.
from the GNU version of the Collaborative International Dictionary of English
 adj. Various in kind or quality; many in number; numerous; multiplied; complicated.
 adj. Exhibited at divers times or in various ways;  used to qualify nouns in the singular number.
 n. A copy of a writing made by the manifold process.
 n. A cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others.
 n. The third stomach of a ruminant animal.
 transitive v. To take copies of by the process of manifold writing.
from The Century Dictionary and Cyclopedia
 Of many kinds; numerous in kind or variety; varied; diverse.
 Exhibiting or embracing many points, features, or characteristics; complicated in character; having many parts or relations: used with nouns in the singular number: as, the manifold wisdom or the manifold grace of God (Eph. iii. 10; 1 Pet. iv. 10); “the manifold use of friendship,”
 n. A complicated object or subject; that which consists of many and various parts; specifically, an aggregate of particulars or units; especially, in mathematics, a multitude of objects connected by a system of relations; an ensemble.
 n. In Kant's theory of knowledge, the total of the particulars furnished by sense before they are connected by the synthesis of the understanding; that which is in the sense and has not yet been in thought.
 n. A copy or facsimile made by means of a manifoldwriter, or by the use of carbonpaper in a typewriter, etc.
 n. A tube, usually of cast metal, with one or more flanged or screwthreaded inlets and two or more flanged or screwthreaded outlets for pipeconnections, much used in pipefitting for steamheating coils, or for coolingcoils in breweries, and in other cases where it is useful to convey steam, water, or air from a large pipe into several smaller ones. Also called Tbranch and header.
 Many times; in multiplied number or quantity.
 To make manifold; multiply; specifically, to multiply impressions of by a single operation, as a letter by means of a manifoldwriter, or by the use of carbonpaper in a typewriter.
 n. In mathematics, given a general conception capable of various determinations or determinationmodes, the totality of the determinable particulars is a manifold, of which each is an element. The manifold is continuous or discrete, according as the passage from one determination to another is continuous or discrete.
 n. Same as manifoldvalve.
 n. The third stomach of a ruminant; the manyplies; the intestines generally.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 v. combine or increase by multiplication
 v. make multiple copies of
 n. a pipe that has several lateral outlets to or from other pipes
 n. a lightweight paper used with carbon paper to make multiple copies
 adj. many and varied; having many features or forms
 n. a set of points such as those of a closed surface or an analogue in three or more dimensions
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

Some informal background: a Riemannian manifold is a differentiable manifold (where the tangent space at each point has an inner product) with a positivedefinite metric tensor, d (x, y) ≥ 0.

A familiar Riemannian manifold is a Euclidean manifold (where one has to add a smoothly varying inner product on the tangent space of the standard Euclidean space), with the familiar Euclidean (distance) metric (our 3space, for example).

The Lorentzian manifold is a pseudoRiemannian manifold, the generalization of the Riemannian manifold, such that the metric tensor need not be positivedefinite.

In my sleep I slew them in manifold ways and threw their carcasses into the reservoir.

They are cultural hybrids, to be sure, combining indigenous traditions with Christian theology in manifold ways.

Then she took her lute and, preluding thereon in manifold modes, lastly returned to the first and sang these couplets,

Each manifold is the virtual manifestation of your own private paradise.

His gutra (not from Dunhill) was tucked in manifold gatherings under the agal, or headband.

Mixing chambers with a larger volume than just a Tjoint pipe provide a longer retention time of air and fuel inside the chamber and a more homogeneous mixture which becomes essential when the distance between mixing device and inlet manifold is short, hence the mixing time.

The last alternative may be easier to manufacture but may also show inferior mixing qualities in cases where the distance to the manifold is short.
npydyuan commented on the word manifold
I love how this word can be both academic and automotive.
September 17, 2007