Trivializable sub-Riemannian structures on spheres
| Autor: | Chisato Iwasaki, Kenro Furutani, Wolfram Bauer |
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| Rok vydání: | 2013 |
| Předmět: |
Pure mathematics
Mathematics(all) Rank (linear algebra) General Mathematics 010102 general mathematics Spectrum (functional analysis) Mathematical analysis Explained sum of squares Clifford module 01 natural sciences symbols.namesake Bracket (mathematics) Distribution (mathematics) 0103 physical sciences symbols Jacobi polynomials Vector field 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Bulletin des Sciences Mathématiques. 137(3):361-385 |
| ISSN: | 0007-4497 |
| DOI: | 10.1016/j.bulsci.2012.09.004 |
| Popis: | We classify the trivializable sub-Riemannian structures on odd-dimensional spheres S N that are induced by a Clifford module structure of R N + 1 . The underlying bracket generating distribution is of step two and spanned by a set of global linear vector fields X 1 , … , X m . As a result we show that such structures only exist in the cases where N = 3 , 7 , 15 . The corresponding hypo-elliptic sub-Laplacians Δ sub are defined as the (negative) sum of squares of the vector fields X j . In the case of a trivializable rank four distribution on S 7 and a trivializable rank eight distribution on S 15 we obtain a part of the spectrum of Δ sub . We also remark that in both cases there is a relation between the eigenfunctions and Jacobi polynomials. |
| Databáze: | OpenAIRE |
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