Tank destroyerA tank destroyer, tank hunter or tank killer is a type of armoured fighting vehicle, predominantly intended for anti-tank duties. As such, they are typically armed with a direct fire artillery gun, then called self-propelled anti-tank gun, or missile launcher, then called anti-tank missile carrier, and designed specifically to engage and destroy enemy tanks, often with limited operational capacities.
Anti-tank warfareAnti-tank warfare originated from the need to develop technology and tactics to destroy tanks during World War I. Since the Allies deployed the first tanks in 1916, the German Empire developed the first anti-tank weapons. The first developed anti-tank weapon was a scaled-up bolt-action rifle, the Mauser 1918 T-Gewehr, that fired a 13.2 mm cartridge with a solid bullet that could penetrate the thin armor of tanks of the time and destroy the engine or ricochet inside, killing occupants.
Connection formIn mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of a coordinate frame, and so is not a tensorial object.
TankA tank is an armoured fighting vehicle intended as a primary offensive weapon in front-line ground combat. Tank designs are a balance of heavy firepower, strong armour, and good battlefield mobility provided by tracks and a powerful engine; usually their main armament is mounted in a turret. They are a mainstay of modern 20th and 21st century ground forces and a key part of combined arms combat.
Connection (vector bundle)In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of a linear connection on a vector bundle, for which the notion of parallel transport must be linear. A linear connection is equivalently specified by a covariant derivative, an operator that differentiates sections of the bundle along tangent directions in the base manifold, in such a way that parallel sections have derivative zero.
Tanks in World War IITanks were an important weapons system in World War II. Even though tanks in the inter-war years were the subject of widespread research, production was limited to relatively small numbers in a few countries. However, during World War II, most armies employed tanks, and production levels reached thousands each month. Tank usage, doctrine and production varied widely among the combatant nations. By war's end, a consensus was emerging regarding tank doctrine and design.
Connection (principal bundle)In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
Valentine tankThe Tank, Infantry, Mk III, Valentine was an infantry tank produced in the United Kingdom during World War II. More than 8,000 of the type were produced in eleven marks, plus various specialised variants, accounting for approximately a quarter of wartime British tank production. The many variants included riveted and welded construction, petrol and diesel engines and a progressive increase in armament. It was supplied in large numbers to the USSR and built under licence in Canada.
Metric connectionIn mathematics, a metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. This is equivalent to: A connection for which the covariant derivatives of the metric on E vanish. A principal connection on the bundle of orthonormal frames of E. A special case of a metric connection is a Riemannian connection; there is a unique such which is torsion free, the Levi-Civita connection.
Tanks in World War IThe development of tanks in World War I was a response to the stalemate that developed on the Western Front. Although vehicles that incorporated the basic principles of the tank (armour, firepower, and all-terrain mobility) had been projected in the decade or so before the War, it was the alarmingly heavy casualties of the start of its trench warfare that stimulated development. Research took place in both Great Britain and France, with Germany only belatedly following the Allies' lead.
