منابع مشابه
Lorentzian Worldlines and Schwarzian Derivative
The aim of this note is to relate the classical Schwarzian derivative and the geometry of Lorentz surfaces of constant curvature. 1. The starting point of our investigations lies in the following remark (joint work with L. Guieu). Consider a curve y = f(x) in the Lorentz plane with metric g = dxdy. If f (x) > 0, then its Lorentz curvature can be computed : ̺(x) = f (x) (f (x)) and enjoys the qui...
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It is customary to formulate the inequalities of the "Verzerrungssatz" type for analytic functions w—f(z), schlicht in the unit circle, with reference to a specific normalization. The two normalizations mainly used are: (a) f(z) is finite in \z\ < 1 , /(O) = 0 , /'(O) = 1; (b) ƒ(z) has a pole at 2 = 0 with the residue 1. If we want to obtain inequalities which are independent of any particular ...
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The main character of the present note is the Schwarzian derivative, and we start with a brief reminder of its definition and main properties. Let f : RP → RP be a projective line diffeomorphism. For every point x ∈ RP there exists a unique projective transformation gx : RP 1 → RP whose 2-jet at x coincides with that of f . The Schwarzian derivative S(f) measures the deviation of the 3-jet jf f...
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The Schwarzian derivative of an analytic function is a basic tool in complex analysis. It appeared as early as 1873, when H. A. Schwarz sought to generalize the Schwarz-Christoffel formula to conformal mappings of polygons bounded by circular arcs. More recently, Nehari [5, 6, 7] and others have developed important criteria for global univalence in terms of the Schwarzian derivative, exploiting...
متن کاملSchwarzian derivative and Numata Finsler structures
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1969
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1969.31.717