Athwart immersions into hyperbolic space
نویسندگان
چکیده
منابع مشابه
The Hyperbolic Plane and its Immersions into R3
The hyperbolic plane is an example of a geometry where the first four of Euclid’s Axioms hold but the fifth, the parallel postulate, fails and is replaced by a hyperbolic alternative. We discuss some basic properties of hyperbolic space, including how to coordinatize and measure lengths. We then consider the possibility of isometrically immersing the hyperbolic plane into 3 in such a way that l...
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Finite order invariants of stable immersions of a closed orientable surface into R have been defined in [N], where all order 1 invariants have been classified. In the present work we classify all finite order invariants of order n > 1, and show that they are all functions of the universal order 1 invariant constructed in [N]. The structure of the paper is as follows: In Section 2 we summarize t...
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We classify all order one invariants of immersions of a closed orientable surface F into R3, with values in an arbitrary Abelian group G. We show that for any F and G and any regular homotopy class A of immersions of F into R3, the group of all order one invariants on A is isomorphic to Gא0 ⊕B⊕B where Gא0 is the group of all functions from a set of cardinality א0 into G and B = {x ∈ G : 2x = 0}...
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Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two clo...
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Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two clo...
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ژورنال
عنوان ژورنال: Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics
سال: 1984
ISSN: 1303-5991
DOI: 10.1501/commua1_0000000575