Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 adjective Many and varied; of many kinds; multiple.
 adjective Having many features or forms.
 adjective Being such for a variety of reasons.
 adjective Consisting of or operating several devices of one kind at the same time.
 noun A whole composed of diverse elements.
 noun One of several copies.
 noun A pipe or chamber having multiple apertures for making connections.
 noun Mathematics A topological space in which each point has a neighborhood that is equivalent to a neighborhood in Euclidean space. The surface of a sphere is a twodimensional manifold because the neighborhood of each point is equivalent to a part of the plane.
 transitive verb To make several copies of, as with carbon paper.
 transitive verb To make manifold; multiply.
from The Century Dictionary.
 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.
 noun 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.
 noun Same as
manifoldvalve .  Many times; in multiplied number or quantity.
 noun The third stomach of a ruminant; the manyplies; the intestines generally.
 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,”
 noun 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.
 noun 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.
 noun A copy or facsimile made by means of a manifoldwriter, or by the use of carbonpaper in a typewriter, etc.
 noun 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.
from the GNU version of the Collaborative International Dictionary of English.
 transitive verb To take copies of by the process of manifold writing.
 noun A copy of a writing made by the manifold process.
 noun (Mech.) A cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others.
 noun Local, U.S. The third stomach of a ruminant animal.
 adjective Various in kind or quality; many in number; numerous; multiplied; complicated.
 adjective Exhibited at divers times or in various ways;  used to qualify nouns in the singular number.
 adjective a process or method by which several copies, as of a letter, are simultaneously made, sheets of coloring paper being infolded with thin sheets of plain paper upon which the marks made by a stylus or a typewriter are transferred; writing several copies of a document at once by use of carbon paper or the like.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 verb transitive To make manifold;
multiply .  verb transitive, printing To multiply or
reproduce impressions of by a single operation.  noun now historical A
copy made by the manifold writing process.  noun mechanics A pipe
fitting or similardevice that connects multipleinputs oroutputs .  noun US, regional, plural The third
stomach of aruminant animal, anomasum .  noun mathematics A
topological space that lookslocally like the "ordinary"Euclidean space and isHausdorff .  adjective
Various inkind orquality ;many in number;numerous ;multiplied ;complicated ;diverse .  adjective
Exhibited at diverse times or in various ways.  adverb Many times;
repeatedly .
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 verb combine or increase by multiplication
 verb make multiple copies of
 noun a pipe that has several lateral outlets to or from other pipes
 noun a lightweight paper used with carbon paper to make multiple copies
 adjective many and varied; having many features or forms
 noun 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
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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.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

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).
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

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).

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.

The Lorentzian manifold is a pseudoRiemannian manifold, the generalization of the Riemannian manifold, such that the metric tensor need not be positivedefinite.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

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.
The Golden Poppy 2010

They are cultural hybrids, to be sure, combining indigenous traditions with Christian theology in manifold ways.
Introduction 2008

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.
npydyuan commented on the word manifold
I love how this word can be both academic and automotive.
September 17, 2007