homothety meaning in Hindi

Examples

1. If A is abelian, the second point of the proposition above is equivalent to the statement, that \ rho ( a ) is a homothety for every a \ in A.
2. A Fubini Study metric is determined up to homothety ( overall scaling ) by invariance under such a U ( " n " + 1 ) action; thus it is homogeneous.
3. Sometimes, by extension, a surface is called a Clifton Pohl torus if it is a finite covering of the quotient of M by any homothety of ratio different from \ pm 1.
4. When " P " does not coincide with the origin, point reflection is equivalent to a special case of homothetic transformation : homothety with homothetic center coinciding with P, and scale factor =-1.
5. The TC may exist even if the body has non-homogeneous isotropic thermal properties, but when this condition is not verified, it's not possible to determine its position by using the simple geometric method shown above, and the transformation will not be a homothety.
6. As \ nabla h = 0, every homothety is an affine and the set of all homotheties on M forms a Lie subalgebra of A ( M ) denoted by H ( M ) ( the "'homothetic algebra "') and satisfies for connected " M"
7. As a consequence, in the specific case in which " S " a " " O ", the homothety becomes a linear transformation, which preserves not only the collinearity of points ( straight lines are mapped to straight lines ), but also vector addition and scalar multiplication.
8. Taking c = 0 in the defining property of a homothety, it is seen that every Killing is a homothety ( and hence an affine ) and the set of all Killing vector fields on M forms a Lie subalgebra of H ( M ) denoted by K ( M ) ( the "'Killing algebra "') and satisfies for connected " M"
9. Taking c = 0 in the defining property of a homothety, it is seen that every Killing is a homothety ( and hence an affine ) and the set of all Killing vector fields on M forms a Lie subalgebra of H ( M ) denoted by K ( M ) ( the "'Killing algebra "') and satisfies for connected " M"