scholarly journals Analytic equivalence of normal crossing functions on a real analytic manifold

2012 ◽  
Vol 104 (6) ◽  
pp. 1121-1170
Author(s):  
Goulwen Fichou ◽  
Masahiro Shiota
Keyword(s):  
Analytic Manifold ◽  
Normal Crossing ◽  
Real Analytic Manifold ◽  
Real Analytic

A Property of Lie Group Orbits

2000 ◽  
Vol 43 (1) ◽  
pp. 47-50
Author(s):  
Mladen Božičević
Keyword(s):  
Lie Group ◽  
Analytic Manifold ◽  
Conormal Variety ◽  
Real Analytic Manifold ◽  
Real Analytic ◽  
Equivariant Sheaf

AbstractLet G be a real Lie group and X a real analytic manifold. Suppose that G acts analytically on X with finitely many orbits. Then the orbits are subanalytic in X. As a consequence we show that the micro-support of a G-equivariant sheaf on X is contained in the conormal variety of the G-action.

scholarly journals Some results on Semisimple Symmetric Spaces and Invariant Differential Operators

2017 ◽  
Vol 116 (2) ◽  
Author(s):  
Trần Đạo Dõng
Keyword(s):  
Symmetric Space ◽  
Open Subset ◽  
Symmetric Spaces ◽  
Differential Operators ◽  
Analytic Manifold ◽  
Invariant Differential Operators ◽  
Semisimple Symmetric Space ◽  
Real Analytic Manifold ◽  
Invariant Differential ◽  
Real Analytic

<pre>Let X = G/H be a semisimple symmetric space of non-compact style. Our purpose is to construct a compact real analytic manifold in which the semisimple symmetric space X = G/H is realized as an open subset and that $G$ acts analytically on it.</pre><pre> By the <span>Cartan</span> decomposition <span>G = KAH,</span> we must <span>compacify</span> the <span>vectorial</span> part <span>A.$</span></pre><pre> In [6], by using the action of the Weyl group, we constructed a compact real analytic manifold in which the semisimple symmetric space G/H is realized as an open subset and that G acts analytically on it.</pre><pre>Our construction is a motivation of the <span>Oshima's</span> construction and it is similar to those in N. <span>Shimeno</span>, J. <span>Sekiguchi</span> for <span>semismple</span> symmetric spaces.</pre><pre>In this note, first we will <span>inllustrate</span> the construction via the case of <span>SL (n, </span>R)/SO_e (1, n-1) and then show that the system of invariant differential operators on X = G/H extends analytically on the corresponding compactification. </pre>

scholarly journals Complexification and Hypercomplexification of Manifolds with a Linear Connection

2003 ◽  
Vol 14 (08) ◽  
pp. 813-824 ◽  
Author(s):  
Roger Bielawski
Keyword(s):  
Vector Fields ◽  
Polar Decomposition ◽  
Twistor Space ◽  
Complex Structure ◽  
Linear Connection ◽  
Analytic Manifold ◽  
Zero Curvature ◽  
Metric Connection ◽  
Real Analytic Manifold ◽  
Real Analytic

We give a simple interpretation of the adapted complex structure of Lempert–Szöke and Guillemin–Stenzel: it is given by a polar decomposition of the complexified manifold. We then give a twistorial construction of an SO(3)-invariant hypercomplex structure on a neighbourhood of X in TTX, where X is a real-analytic manifold equipped with a linear connection. We show that the Nahm equations arise naturally in this context: for a connection with zero curvature and arbitrary torsion, the real sections of the twistor space can be obtained by solving Nahm's equations in the Lie algebra of certain vector fields. Finally, we show that, if we start with a metric connection, then our construction yields an SO(3)-invariant hyperkähler metric.

scholarly journals Deformations of real analytic functions and the natural stratification of the space of real analytic functions

1976 ◽  
Vol 63 ◽  
pp. 139-152
Author(s):  
Takuo Fukuda
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Real Analytic Function ◽  
Analytic Manifold ◽  
Analytic Set ◽  
Real Analytic Functions ◽  
Real Analytic Manifold ◽  
Real Analytic

Let A be a real analytic set, M be a compact real analytic manifold and f : A × M → R be a real analytic function. Then we have a family of real analytic functions fa, a ∈ A, on M defined by fa(X) = f(a, x).

Explicit invariant solutions for invariant linear differential operators

1984 ◽  
Vol 98 (1-2) ◽  
pp. 149-166 ◽  
Author(s):  
Zofia Szmydt ◽  
Bogdan Ziemian
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Linear Differential Operator ◽  
Invariant Solution ◽  
Real Analytic Function ◽  
Linear Differential Operators ◽  
Invariant Distributions ◽  
Real Analytic Manifold ◽  
Real Analytic ◽  
Linear Differential

SynopsisLet F be a real analytic function on a real analytic manifold X. Let P be a linear differential operator on X such that , where Q is an ordinary differential operator with analytic coefficients whose singular points are all regular. For each (isolated) critical value z of F, we construct locally an F-invariant solution u of the equation Pu - v, v being an arbitrary F-invariant distribution supported in F−1(z). The solution u is constructed explicitly in the form of a series of F-invariant distributions.

The Analyticity of Kernels

1961 ◽  
Vol 13 ◽  
pp. 645-649 ◽  
Author(s):  
J. De Barros-Neto ◽  
F. E. Browder
Keyword(s):  
Linear Space ◽  
Compact Support ◽  
Dual Space ◽  
Inductive Limit ◽  
Differentiable Functions ◽  
Real Analytic Functions ◽  
Infinitely Differentiable Functions ◽  
Inductive Limit Topology ◽  
Real Analytic Manifold ◽  
Real Analytic

Let V be a paracompact real analytic manifold of dimension n ≥ 1. Following the terminology of the theory of distributions of Schwartz (4), is the linear space of infinitely differentiable functions with compact support in V with the appropriate inductive limit topology, is the Frechet space of infinitely differentiable functions on V, is the dual space of consisting of the distributions on V, the dual space of consisting of the distributions with compact support on V. Let 𝒰(V) be the linear space of real analytic functions on V.

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