induced metric उदाहरण वाक्य
उदाहरण वाक्य
- 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.