Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A manifold which is a subset of another, so that the inclusion function is an embedding or, sometimes, an immersion

from The Century Dictionary and Cyclopedia

  • n. The selected elements of a partitioned manifold.

Etymologies

Sorry, no etymologies found.

Examples

  • This would include: the formation and decay of (nonsupersymmetric) black holes; graviton scattering at hyper-Planckian energies; physically continuous transitions from one topology, through a quantum state with no geometric interpretation, to a different topology; states where a submanifold of spacetime has a noncommutative geometry; states with a variety of apparent geometric singularities, where the physics is nonsingular.

    Guest Post: Joe Polchinski on Science or Sociology?

  • The general hypothesis is that the universe as a whole is 3+1+d dimensional (so that there are d extra, spatial dimensions), with gravity propagating in all dimensions, but the standard model fields confined to a 3+1 dimensional submanifold that comprises our observable universe.

    Model Building and Naturalness

  • In this model, matter fields are confined to a four-dimensional submanifold and gravity is described by two different terms; one five-dimensional gravitational action and another four-dimensional action.

    From Quantum to Cosmos-II

  • This submanifold is called the brane (as in membrane).

    Model Building and Naturalness

  • The general hypothesis is that the universe as a whole is 3+1+d dimensional (so that there are d extra spatial dimensions), with gravity propagating in all dimensions, but the standard model fields confined to a 3+1 dimensional submanifold that comprises our observable universe.

    Identifying Dark Matter

  • There are also other, field-theoretic, ways of localizing matter on a submanifold, by using a topological defect.

    Identifying Dark Matter

  • Start with a three-manifold Σ equipped with quantities which, when Σ is embedded as a spacelike submanifold of spacetime, become initial data for the vacuum field equations.

    Time Machines

  • In their version of manifold learning, they assume that the space of target functions (e.g. all possible classifiers), consists of functions supported on a submanifold † † of the original high-dimensional euclidean/feature space.

    O'Reilly News

  • It’s really just a topological surface, and its action functional is just its area as a submanifold of spacetime.

    Not Even Wrong

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