analytic manifold造句

• This definition is mostly used when discussing analytic manifolds in algebraic geometry.
• His dissertation was titled " On complex analytic manifolds with Kahler metric ".
• Numerous minimality results for complex analytic manifolds are based on the Wirtinger inequality for 2-forms.
• Considered as a real 2-dimensional analytic manifold, the open unit disk is therefore isomorphic to the whole plane.
• The long line or ray can even be equipped with the structure of a ( real ) analytic manifold ( with boundary in the case of the closed ray ).
• Every Riemann surface is a two-dimensional real analytic manifold ( i . e ., a complex structure ) which is needed for the unambiguous definition of holomorphic functions.
• As it is an differentiable function, and even an analytic function ( outside of zero ), the real projective line is both a differentiable manifold and an analytic manifold.
• For example the equation y ^ 3 + 2 x ^ 2 y-x ^ 4 = 0 defines a real analytic manifold but has a singular point at the origin.
• For example, in the sheaf of analytic functions on an analytic manifold, a germ of a function at a point determines the function in a small neighborhood of a point.
• However, this is much more difficult than for the differentiable case ( it depends on the classification of ( separable ) one-dimensional analytic manifolds, which is more difficult than for differentiable manifolds ).
• Let G \ subset { \ mathbb { C } } ^ n be a domain ( an set ), or alternatively for a more general definition, let G be an n dimensional complex analytic manifold.
• If X is a C ^ k manifold ( i . e ., a manifold whose analytic manifold ( i . e . infinitely differentiable and charts are expressible as power series ), and \ gamma is an analytic map, then \ gamma is said to be an " analytic curve ".
• A "'Finsler manifold "'allows the definition of distance but does not require the concept of angle; it is an analytic manifold in which each tangent space is equipped with a metric, defining the length of a curve; but it cannot in general be used to define an inner product.
• By contrast, the existence of the Pr黤er surface shows that there exist two-dimensional complex manifolds ( which are necessarily 4-dimensional real manifolds ) with no countable base . ( This is because any " n "-real-dimensional real-analytic manifold " Q " can be extended to an " n "-complex-dimensional complex manifold " W " that contains " Q " as a real-analytic submanifold .)