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nonorientable space

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  • Surface — This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X , Y , and Z contours shown. In mathematics,… …   Wikipedia

  • topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …   Universalium

  • Orientability — For orientation of vector spaces, see orientation (mathematics). For other uses, see Orientation (disambiguation). The torus is an orientable surface …   Wikipedia

  • Introduction to systolic geometry — Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside a closed curve C , and the length or perimeter of C . Since the area A may be small while the… …   Wikipedia

  • Systolic geometry — In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner, and developed by Mikhail Gromov and others, in its arithmetic, ergodic, and topological manifestations.… …   Wikipedia

  • Elliptic geometry — (sometimes known as Riemannian geometry) is a non Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p.Elliptic geometry, like hyperbolic geometry, violates Euclid s parallel… …   Wikipedia

  • Rips machine — In geometric group theory, the Rips machine is a method of studying the action of groups on R trees. It was introduced in unpublished work of Eliyahu Rips in about 1991. An R tree is a uniquely arcwise connected metric space in which every arc is …   Wikipedia

  • Volume form — In mathematics, a volume form is a nowhere zero differential n form on an n manifold. Every volume form defines a measure on the manifold, and thus a means to calculate volumes in a generalized sense. A manifold has a volume form if and only if… …   Wikipedia

  • Non-orientable wormhole — In wormhole theory, a non orientable wormhole is a wormhole connection that appears to reverse the chirality of anything passed through it. It is related to the twisted connections normally used to construct a Möbius strip or Klein bottle. In… …   Wikipedia

  • Loewner's torus inequality — In differential geometry, Loewner s torus inequality is an inequality due to Charles Loewner for the systole of an arbitrary Riemannian metric on the 2 torus.tatementIn 1949 Charles Loewner proved that every metric on the 2 torus mathbb T^2… …   Wikipedia

  • Pu's inequality — [ Roman Surface representing RP2 in R3] In differential geometry, Pu s inequality is an inequality proved by P. M. Pu for the systole of an arbitrary Riemannian metric on the real projective plane RP2.tatementA student of Charles Loewner s, P.M.… …   Wikipedia

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