submanifold

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? Sean 2007

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 Mark 2006

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

Model Building and Naturalness Mark 2006

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 Mark 2006

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

Identifying Dark Matter Mark 2006

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 Mark 2006

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

Identifying Dark Matter Mark 2006

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 Earman, John 2004

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 2010

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 2010