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  1. Science in China Series A: Mathematics
  2. Science in China Series A: Mathematics : Volume 48
  3. Science in China Series A: Mathematics : Volume 48, Issue 1, Supplement,December 2005
  4. Transformations and non-degenerate maps
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Science in China Series A: Mathematics : Volume 60
Science in China Series A: Mathematics : Volume 59
Science in China Series A: Mathematics : Volume 58
Science in China Series A: Mathematics : Volume 57
Science in China Series A: Mathematics : Volume 56
Science in China Series A: Mathematics : Volume 55
Science in China Series A: Mathematics : Volume 54
Science in China Series A: Mathematics : Volume 53
Science in China Series A: Mathematics : Volume 52
Science in China Series A: Mathematics : Volume 51
Science in China Series A: Mathematics : Volume 50
Science in China Series A: Mathematics : Volume 49
Science in China Series A: Mathematics : Volume 48
Science in China Series A: Mathematics : Volume 48, Issue 12, December 2005
Science in China Series A: Mathematics : Volume 48, Issue 1, Supplement,December 2005
Multiplier ideal sheaves in complex and algebraic geometry
Weighted composition operators and locally convex algebras
Complex geometry: Its brief history and its future
Integral formulas and the ohsawa-takegoshi extension theorem
CR deformations for rational homogeneous surface singularities
Functions on discrete sets holomorphic in the sense of isaacs, or monodiffric functions of the first kind
Geometric aspects of the moduli space of riemann surfaces
On holomorphic immersions into kähler manifolds of constant holomorphic sectional curvature
Nevanlinna theory and diophantine approximation
Degeneracy of holomorphic curves in surfaces
Adiabatic paths and pseudoholomorphic curves
Equidistribution for meromorphic transforms and the dd$^{c}$-method
Transformations and non-degenerate maps
Complex geometry and real geometry
Immortal solution of the Ricci flow
Weighted Bergman kernels and virtual Bergman kernels
Ritt’s theorem and the Heins map in hyperbolic complex manifolds
On uniform estimate in Calabi-Yau theorem
Examples of unbounded homogeneous domains in complex space
Some remarks on the genericity of unique range sets for meromorphic functions
Automorphism groups of causal symmetric spaces of Cayley type and bounded symmetric domains
P-twisted affine Lie algebra and its realiza tions by twisted vertex operators
Randomization of Q$_{p}$ spaces on the unit ball of ℂ$^{n}$
Proper holomorphic self-maps of smooth bounded Reinhardt domains in ℂ$^{n}$
A boundary value problem for hypermonogenic functions in Clifford analysis
Almansi decomposition for Dunkl operators
Extremal problems on the Hua domain of the first type
Normal families of meromorphic mappings of several complex variables into P$^{N}$ (C) for moving targets
The computations of Einstein-Kähler metric of Cartan-Hartogs domain
Horizontal $$\bar \partial $$ -Laplacian on complex Finsler manifolds-Laplacian on complex Finsler manifolds
On the composition operators on the Bloch space of several complex variables
Bergman kernel function on Hua Construction of the second type
Bergman kernel function on the third Hua Construction
Science in China Series A: Mathematics : Volume 48, Issue 11, November 2005
Science in China Series A: Mathematics : Volume 48, Issue 10, October 2005
Science in China Series A: Mathematics : Volume 48, Issue 9, September 2005
Science in China Series A: Mathematics : Volume 48, Issue 8, August 2005
Science in China Series A: Mathematics : Volume 48, Issue 7, July 2005
Science in China Series A: Mathematics : Volume 48, Issue 6, June 2005
Science in China Series A: Mathematics : Volume 48, Issue 5, May 2005
Science in China Series A: Mathematics : Volume 48, Issue 4, April 2005
Science in China Series A: Mathematics : Volume 48, Issue 3, March 2005
Science in China Series A: Mathematics : Volume 48, Issue 2, February 2005
Science in China Series A: Mathematics : Volume 48, Issue 1, January 2005
Science in China Series A: Mathematics : Volume 47
Science in China Series A: Mathematics : Volume 46
Science in China Series A: Mathematics : Volume 45
Science in China Series A: Mathematics : Volume 44
Science in China Series A: Mathematics : Volume 43
Science in China Series A: Mathematics : Volume 42
Science in China Series A: Mathematics : Volume 41
Science in China Series A: Mathematics : Volume 40

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Transformations and non-degenerate maps

Content Provider Springer Nature Link
Author Li, Baokui Wang, Yuefei
Copyright Year 2005
Abstract We shall prove the equivalences of a non-degenerate circle-preserving map and a Möbius transformation in $$\hat {\mathbb{R}}^n $$ , of a non-degenerate geodesic-preserving map and an isometry in ℍ$^{n}$, of a non-degenerate line-preserving map and an affine transformation in ℝ$^{n}$. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.
Starting Page 195
Ending Page 205
Page Count 11
File Format PDF
ISSN 10069283
Journal Science in China Series A: Mathematics
Volume Number 48
Issue Number 1
e-ISSN 18622763
Language English
Publisher Science in China Press
Publisher Date 2005-01-01
Publisher Place Beijing
Access Restriction Subscribed
Subject Keyword Möbius transformation circle-preserving map non-degenerate map Applications of Mathematics
Content Type Text
Resource Type Article
Subject Mathematics
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