Extension of Riemannian metrics and growth-type

Renata Grimaldi; Ignazia Maniscalco

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 3, page 213-220
  • ISSN: 1120-6330

Abstract

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Let M be a noncompact differentiable manifold and V an open proper submanifold endowed with a complete Riemannian metric g . We prove that g can be extended all over M to a complete Riemannian metric G having the same growth-type as g .

How to cite

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Grimaldi, Renata, and Maniscalco, Ignazia. "Extension de métriques riemanniennes et type de croissance." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.3 (1998): 213-220. <http://eudml.org/doc/252363>.

@article{Grimaldi1998,
author = {Grimaldi, Renata, Maniscalco, Ignazia},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Riemannian metrics; Geodesic balls; Volume; Riemannian metric; normal bundle; growth-type},
language = {fre},
month = {9},
number = {3},
pages = {213-220},
publisher = {Accademia Nazionale dei Lincei},
title = {Extension de métriques riemanniennes et type de croissance},
url = {http://eudml.org/doc/252363},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Grimaldi, Renata
AU - Maniscalco, Ignazia
TI - Extension de métriques riemanniennes et type de croissance
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/9//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 3
SP - 213
EP - 220
LA - fre
KW - Riemannian metrics; Geodesic balls; Volume; Riemannian metric; normal bundle; growth-type
UR - http://eudml.org/doc/252363
ER -

References

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  2. Cheeger, J. - Ebin, D., Comparison theorems in Riemannian Geometry. North-Holland1975. Zbl0309.53035MR458335
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  7. Grimaldi, R. - Pansu, P., Sur le type de croissance des métriques de révolution. C. R. Acad. Sc. Paris, 311, Sér. I, 1990, 889-892. Zbl0724.53024MR1084048
  8. Grimaldi, R. - Pansu, P., Sur la croissance du volume dans une classe conforme. Jour. Math. pures et appl., 71, 1992, 1-19. Zbl0667.53034MR1151555
  9. Grimaldi, R. - Pansu, P., Sur la régularité de la fonction croissance d’une variété riemannienne. Geometriae Dedicata, 50, 1994, 301-307. Zbl0812.53040MR1286383DOI10.1007/BF01267872
  10. Grimaldi, R. - Pansu, P., Sur le degré de différentiabilité de la fonction croissance en dimension deux. Boll. U.M.I., (7) 11-B, 1997, Suppl. fasc. 2, 25-38. Zbl0880.53031MR1456249
  11. Gromov, M., Volume and bounded cohomology. Publ. I.H.E.S., 56, 1982, 5-100. Zbl0516.53046MR686042
  12. Hirsch, M., Differential Topology. Springer-Verlag, Berlin-Heidelberg1976. Zbl0356.57001MR448362

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