holomorphic map sentence in Hindi
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- The zero set of this section consists of holomorphic maps.
- The composition of two holomorphic maps is holomorphic.
- Do you mean a subgroup of holomorphic maps?
- This group can be given the structure of a complex manifold in such a way that composition and inversion are holomorphic maps.
- :: Yes, I meant to say the subgroup whose members are holomorphic maps rather than calling the subgroup itself holomorphic.
- Accordingly, ?! } } is a smooth diffeomorphism, which restricts to a holomorphic map and a smooth diffeomorphism between the boundaries.
- "[ at the conference ] . . . Bott and I learnt of a conjecture of Shimura concerning a generalization of the Lefschetz formula for holomorphic maps.
- Moreover the changes of charts are holomorphic maps, more precisely maps of the form z \ mapsto z + w for some w \ in \ mathbb C.
- Which is defined by counting holomorphic triangles ( that is, holomorphic maps of a triangle whose vertices and edges map to the appropriate intersection points and Lagrangian submanifolds ).
- The Schwarz & ndash; Pick theorem then essentially states that a holomorphic map of the unit disk into itself " decreases " the distance of points in the Poincar?metric.
- 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 ).
- 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.
- 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 " '.
- 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 " ?.
- 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.
- 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.
- 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 ".
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