Small sub-Riemannian balls onR3 View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1996-07

AUTHORS

El-H. Ch. El-Alaoui, J. -P. Gauthier, I. Kupka

ABSTRACT

This paper deals with sub-Riemannian metrics onR3 in the contact case. We study the singularities of the exponential mapping in the neighborhood of its pole. This is in stark contrast with the Riemannian case where this situation never occurs.

PAGES

359-421

References to SciGraph publications

Journal

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02269424

DOI

http://dx.doi.org/10.1007/bf02269424

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1002116143


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "author": [
      {
        "affiliation": {
          "name": [
            "INSA de Rouen, Department of Mathematics, LMI, URA CNRS D 1378, Pl. E. Blondel, BP 08, 76131, Mont Saint Aignan cedex, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "El-Alaoui", 
        "givenName": "El-H. Ch.", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Laboratoire de Math\u00e9matiques, AMS-LMI, URA CNRS 1378, INSA de Rouen, Place Emile Blondel, BP08, 76131, Mont-Saint-Aignan Cedex, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Gauthier", 
        "givenName": "J. -P.", 
        "id": "sg:person.010301262074.33", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010301262074.33"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Sorbonne University", 
          "id": "https://www.grid.ac/institutes/grid.462844.8", 
          "name": [
            "Department of Mathematics, University of Paris VI, 4 Pl. Jussieu, 75232, Paris cedes 05, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kupka", 
        "givenName": "I.", 
        "id": "sg:person.015316565521.89", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015316565521.89"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-3-642-65505-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043902088", 
          "https://doi.org/10.1007/978-3-642-65505-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-65505-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043902088", 
          "https://doi.org/10.1007/978-3-642-65505-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0393-0440(88)90032-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047418802"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0393-0440(88)90032-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047418802"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0363012993244945", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062880969"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1970595", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069675913"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/jdg/1214440436", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084459573"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-0348-9078-6_144", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1103637207", 
          "https://doi.org/10.1007/978-3-0348-9078-6_144"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1996-07", 
    "datePublishedReg": "1996-07-01", 
    "description": "This paper deals with sub-Riemannian metrics onR3 in the contact case. We study the singularities of the exponential mapping in the neighborhood of its pole. This is in stark contrast with the Riemannian case where this situation never occurs.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf02269424", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1052643", 
        "issn": [
          "1079-2724", 
          "1573-8698"
        ], 
        "name": "Journal of Dynamical and Control Systems", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2"
      }
    ], 
    "name": "Small sub-Riemannian balls onR3", 
    "pagination": "359-421", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "0a13e28d3e8a1dad8ef7db6e8f085065319f9c72c24e8f051b000be09279bda7"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf02269424"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1002116143"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf02269424", 
      "https://app.dimensions.ai/details/publication/pub.1002116143"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T12:42", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000363_0000000363/records_70058_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF02269424"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02269424'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02269424'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02269424'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02269424'


 

This table displays all metadata directly associated to this object as RDF triples.

90 TRIPLES      20 PREDICATES      31 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf02269424 schema:author N34da1f6fea984d4fb3e087260dee1229
2 schema:citation sg:pub.10.1007/978-3-0348-9078-6_144
3 sg:pub.10.1007/978-3-642-65505-0
4 https://doi.org/10.1016/0393-0440(88)90032-0
5 https://doi.org/10.1137/s0363012993244945
6 https://doi.org/10.2307/1970595
7 https://doi.org/10.4310/jdg/1214440436
8 schema:datePublished 1996-07
9 schema:datePublishedReg 1996-07-01
10 schema:description This paper deals with sub-Riemannian metrics onR3 in the contact case. We study the singularities of the exponential mapping in the neighborhood of its pole. This is in stark contrast with the Riemannian case where this situation never occurs.
11 schema:genre research_article
12 schema:inLanguage en
13 schema:isAccessibleForFree false
14 schema:isPartOf N8238edf2e6e3495bbd68a6456eaf3147
15 Nfa68a2eddbb94ab2baf1112c3f982bbb
16 sg:journal.1052643
17 schema:name Small sub-Riemannian balls onR3
18 schema:pagination 359-421
19 schema:productId N209021f699e74fa791ac2b86c9bc3dc3
20 N5dbb42cfba3841a8bda7ed6b7a95f782
21 N778737c628f74c7eb767e12a3712266f
22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002116143
23 https://doi.org/10.1007/bf02269424
24 schema:sdDatePublished 2019-04-11T12:42
25 schema:sdLicense https://scigraph.springernature.com/explorer/license/
26 schema:sdPublisher N374a95ee501c4c14bb5ab265c4e0571c
27 schema:url http://link.springer.com/10.1007/BF02269424
28 sgo:license sg:explorer/license/
29 sgo:sdDataset articles
30 rdf:type schema:ScholarlyArticle
31 N209021f699e74fa791ac2b86c9bc3dc3 schema:name readcube_id
32 schema:value 0a13e28d3e8a1dad8ef7db6e8f085065319f9c72c24e8f051b000be09279bda7
33 rdf:type schema:PropertyValue
34 N34da1f6fea984d4fb3e087260dee1229 rdf:first Nc6dd615200be407b8dccba72d4f64b3b
35 rdf:rest N9b242b52338e4909a6455044b86234e0
36 N374a95ee501c4c14bb5ab265c4e0571c schema:name Springer Nature - SN SciGraph project
37 rdf:type schema:Organization
38 N5867f10600ad48fba133529454a70fcf schema:name Laboratoire de Mathématiques, AMS-LMI, URA CNRS 1378, INSA de Rouen, Place Emile Blondel, BP08, 76131, Mont-Saint-Aignan Cedex, France
39 rdf:type schema:Organization
40 N5dbb42cfba3841a8bda7ed6b7a95f782 schema:name doi
41 schema:value 10.1007/bf02269424
42 rdf:type schema:PropertyValue
43 N778737c628f74c7eb767e12a3712266f schema:name dimensions_id
44 schema:value pub.1002116143
45 rdf:type schema:PropertyValue
46 N8238edf2e6e3495bbd68a6456eaf3147 schema:volumeNumber 2
47 rdf:type schema:PublicationVolume
48 N9b242b52338e4909a6455044b86234e0 rdf:first sg:person.010301262074.33
49 rdf:rest N9cc506c4fc5e44c19fcbcc55e807f1e8
50 N9cc506c4fc5e44c19fcbcc55e807f1e8 rdf:first sg:person.015316565521.89
51 rdf:rest rdf:nil
52 N9d51f396a6e54020a371b6dc1d644498 schema:name INSA de Rouen, Department of Mathematics, LMI, URA CNRS D 1378, Pl. E. Blondel, BP 08, 76131, Mont Saint Aignan cedex, France
53 rdf:type schema:Organization
54 Nc6dd615200be407b8dccba72d4f64b3b schema:affiliation N9d51f396a6e54020a371b6dc1d644498
55 schema:familyName El-Alaoui
56 schema:givenName El-H. Ch.
57 rdf:type schema:Person
58 Nfa68a2eddbb94ab2baf1112c3f982bbb schema:issueNumber 3
59 rdf:type schema:PublicationIssue
60 sg:journal.1052643 schema:issn 1079-2724
61 1573-8698
62 schema:name Journal of Dynamical and Control Systems
63 rdf:type schema:Periodical
64 sg:person.010301262074.33 schema:affiliation N5867f10600ad48fba133529454a70fcf
65 schema:familyName Gauthier
66 schema:givenName J. -P.
67 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010301262074.33
68 rdf:type schema:Person
69 sg:person.015316565521.89 schema:affiliation https://www.grid.ac/institutes/grid.462844.8
70 schema:familyName Kupka
71 schema:givenName I.
72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015316565521.89
73 rdf:type schema:Person
74 sg:pub.10.1007/978-3-0348-9078-6_144 schema:sameAs https://app.dimensions.ai/details/publication/pub.1103637207
75 https://doi.org/10.1007/978-3-0348-9078-6_144
76 rdf:type schema:CreativeWork
77 sg:pub.10.1007/978-3-642-65505-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043902088
78 https://doi.org/10.1007/978-3-642-65505-0
79 rdf:type schema:CreativeWork
80 https://doi.org/10.1016/0393-0440(88)90032-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047418802
81 rdf:type schema:CreativeWork
82 https://doi.org/10.1137/s0363012993244945 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062880969
83 rdf:type schema:CreativeWork
84 https://doi.org/10.2307/1970595 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069675913
85 rdf:type schema:CreativeWork
86 https://doi.org/10.4310/jdg/1214440436 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084459573
87 rdf:type schema:CreativeWork
88 https://www.grid.ac/institutes/grid.462844.8 schema:alternateName Sorbonne University
89 schema:name Department of Mathematics, University of Paris VI, 4 Pl. Jussieu, 75232, Paris cedes 05, France
90 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...