An elliptic surface is a surface equipped with an elliptic fibration ( a surjective holomorphic map to a curve " B " such that all but finitely many fibers are smooth irreducible curves of genus 1 ).
12.
This is a smooth diffeomorphism of } } onto the closed annulus " z " d " 1 } }, restricting to a holomorphic map in the interior and a smooth diffeomorphism on both boundary curves.
13.
In fact, M yields a duality ( contravariant equivalence ) between the category of compact connected Riemann surfaces ( with non-constant holomorphic maps as morphisms ) and function fields of one variable over "'C " '.
14.
Let ? be a bounded region in "'C "'with smooth boundary " ? and let ? be a univalent holomorphic map of the unit disk " D " onto ? extending to a smooth diffeomorphism of the circle onto " ?.
15.
If equality holds throughout in one of the two inequalities above ( which is equivalent to saying that the holomorphic map preserves the distance in the Poincar?metric ), then " f " must be an analytic automorphism of the unit disc, given by a M�bius transformation mapping the unit disc to itself.
16.
This geometry, and associated symmetry group, was studied by Felix Klein as the monodromy groups of a Belyi surface a Riemann surface with a holomorphic map to the Riemann sphere, ramified only at 0, 1, and infinity ( a Belyi function ) the cusps are the points lying over infinity, while the vertices and the centers of each edge lie over 0 and 1; the degree of the covering ( number of sheets ) equals 5.
17.
The Klein surfaces form a category; a morphism from the Klein surface " X " to the Klein surface " Y " is a differentiable map " f " : " X " ?! " Y " which on each coordinate patch is either holomorphic or the complex conjugate of a holomorphic map and furthermore maps the boundary of " X " to the boundary of " Y ".
How to say holomorphic map in Hindi and what is the meaning of holomorphic map in Hindi? holomorphic map Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
