induced metric वाक्य
उदाहरण वाक्य
मोबाइल
- The induced metric on this submanifold,
- A separable measure space has a natural quotient set can be properly metrized by the induced metric.
- There remains ambiguity in the action up to an arbitrary functional of the induced metric h _ { ab }.
- Because the induced metric is fixed on \ partial \ mathcal { M }, the only quantity to be varied is K is the trace of the extrinsic curvature.
- The precise form of the Hartle Hawking state is the path integral over all " D "-dimensional geometries that have the required induced metric on their boundary.
- It is the Hausdorff distance between the unit balls of the two C *-algebras, under the norm-induced metric on the space of all bounded operators on that Hilbert space.
- In mathematics, a "'polar action "'is a proper and flat with respect to the induced metric, then the action is called "'hyperpolar " '.
- A point " p " in a Riemannian submanifold is umbilical if, at " p ", the ( vector-valued ) Second fundamental form is some normal vector tensor the induced metric ( First fundamental form ).
- Although the induced metric of g _ 1 and g _ 2 will agree on \ Sigma _ 2, the normal derivative of g _ 1 at \ Sigma _ 2 will not in general be equal to that of g _ 2 at \ Sigma _ 2.
- X ^ \ mu ( \ xi ) is the field on the worldsheet describing the embedding of the string in 25 + 1 spacetime; in the Polyakov formulation, g is not to be understood as the induced metric from the embedding, but as an independent dynamical field.
- If ? is a doubly connected planar region, then there is a diffeomorphism " F " of an annulus " r " d " | z | d " 1 onto the closure of ?, such that after a conformal change the induced metric on the annulus can be continued smoothly by reflection in both boundaries.
- A remarkable feature of complex geometry is that holomorphic sectional curvature decreases on complex submanifolds . ( The same goes for a more general concept, holomorphic bisectional curvature . ) For example, every complex submanifold of "'C " "'n " ( with the induced metric from "'C " "'n " ) has holomorphic sectional curvature d " 0.
- Here we utilized the cross-normalization condition l ^ an _ a = n ^ al _ a =-1 as well as the requirement that g _ { ab } + l _ an _ b + n _ al _ b should span the induced metric h _ { AB } for cross-sections of { v = constant, r = constant }, where dv and dr are not mutually orthogonal.
- In the ADM formulation of general relativity one splits spacetime into spatial slices and time, the basic variables are taken to be the induced metric, q _ { ab } ( x ), on the spatial slice ( the metric induced on the spatial slice by the spacetime metric ), and its conjugate momentum variable related to the extrinsic curvature, K ^ { ab } ( x ), ( this tells us how the spatial slice curves with respect to spacetime and is a measure of how the induced metric evolves in time ).
- In the ADM formulation of general relativity one splits spacetime into spatial slices and time, the basic variables are taken to be the induced metric, q _ { ab } ( x ), on the spatial slice ( the metric induced on the spatial slice by the spacetime metric ), and its conjugate momentum variable related to the extrinsic curvature, K ^ { ab } ( x ), ( this tells us how the spatial slice curves with respect to spacetime and is a measure of how the induced metric evolves in time ).
- Where \ mathcal { S } _ \ mathrm { EH } is the Einstein Hilbert action, \ mathcal { S } _ \ mathrm { GHY } is the Gibbons Hawking York boundary term, h _ { ab } is the induced metric ( see section below on definitions ) on the boundary, h its determinant, K is the trace of the second fundamental form, \ epsilon is equal to + 1 where \ partial \ mathcal { M } is timelike and-1 where \ partial \ mathcal { M } is spacelike, and y ^ a are the coordinates on the boundary.
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